---
title: "AP Physics C: Mechanics Unit 5 Review: Torque & Rotation"
description: "AP Physics C: Mechanics Unit 5 covers Rotation, Connecting Linear and Rotational Motion, and Torque. Study guides, practice questions, and key terms."
canonical: "https://fiveable.me/ap-physics-c-mechanics/unit-5"
type: "unit"
subject: "AP Physics C: Mechanics"
unit: "Unit 5 – Torque and Rotational Motion"
---

# AP Physics C: Mechanics Unit 5 Review: Torque & Rotation

## Overview

Unit 5 covers rotational kinematics, the linear-rotational connection, torque as a cross product, rotational inertia by integration and the parallel axis theorem, rotational equilibrium, and Newton's second law in the form sum-tau equals I-alpha. It carries 10-15% of the AP exam weight and requires both conceptual reasoning and calculus-based problem solving.

## AP CED Alignment

This unit hub is organized around AP Course and Exam Description topics, skills, and exam task types when they are available in the source data.
- Topic 5.1: Rotational Kinematics
- Topic 5.2: Connecting Linear and Rotational Motion
- Topic 5.3: Torque
- Topic 5.4: Rotational Inertia
- Topic 5.5: Rotational Equilibrium and Newton's First Law in Rotational Form
- Topic 5.6: Newton's Second Law in Rotational Form
- Practice 3: Scientific Questioning and Argumentation
- FRQ 1 – Mathematical Routines
- FRQ 4 – Qualitative/Quantitative Translation
- FRQ 2 – Translation Between Representations

## Topics

- [Topic 5.1: Rotational Kinematics](/ap-physics-c-mechanics/unit-5/1-rotation/study-guide/0tVqvv29lj9DIxVt): Defines angular displacement (delta-theta in radians), angular velocity (omega = d-theta/dt), and angular acceleration (alpha = d-omega/dt). For constant alpha, the four kinematic equations apply directly. Graph interpretation follows the same slope-and-area rules as linear kinematics.
- [Topic 5.2: Connecting Linear and Rotational Motion](/ap-physics-c-mechanics/unit-5/2-connecting-linear-and-rotational-motion/study-guide/79Ym6NXzWOJH6ZWx): Links angular quantities to the linear motion of a point at radius r: s = r*theta, v = r*omega, a_T = r*alpha. All points on a rigid body share omega and alpha, but linear speeds differ by radius. The no-slip condition v_cm = R*omega applies to rolling objects.
- [Topic 5.3: Torque](/ap-physics-c-mechanics/unit-5/3-torque/study-guide/kQhoEJrKtYjpul5K): Torque is the cross product tau = r x F with magnitude rF sin-theta. Only the force component perpendicular to r produces torque. The lever arm is the perpendicular distance from the axis to the line of action of the force. Direction is determined by the right-hand rule.
- [Topic 5.4: Rotational Inertia](/ap-physics-c-mechanics/unit-5/4-rotational-inertia/study-guide/lSrDkHqB6EviD5CA): Rotational inertia I = mr^2 for a point mass, I = integral r^2 dm for continuous solids, and I' = I_cm + Md^2 via the parallel axis theorem. Mass farther from the axis contributes more. AP Physics C requires calculus-based derivations for rods, disks, cylindrical shells, and annular rings.
- [Topic 5.5: Rotational Equilibrium and Newton's First Law in Rotational Form](/ap-physics-c-mechanics/unit-5/5-rotational-equilibrium-and-newtons-first-law-in-rotational-form/study-guide/hkkIAh5Csy8T6d0p): When sum-tau = 0, angular velocity is constant: this is Newton's first law for rotation. Rotational and translational equilibrium are independent conditions. Choosing a strategic pivot eliminates unknown forces from the torque equation.
- [Topic 5.6: Newton's Second Law in Rotational Form](/ap-physics-c-mechanics/unit-5/6-newtons-second-law-in-rotational-form/study-guide/VuXCF8dn0RYwBEaK): When net torque is nonzero, alpha = sum-tau / I_sys. For combined translational and rotational systems, write separate sum-F = ma and sum-tau = I*alpha equations, then connect them with a constraint equation such as a = alpha*R.

## Hardest Topics And Analytics

Snapshot: practice snapshot
This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.
- **63% average MCQ accuracy** (Across 2.3k multiple-choice practice attempts for this unit.)
- **2.3k MCQ attempts** (Practice activity included in this snapshot.)
- **3% average FRQ score** (Across 4 scored free-response attempts for this unit.)
- **Topic 5.4: Rotational Inertia**: 45% MCQ miss rate across 442 attempts. Review Rotational Inertia with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 5.1: Rotational Kinematics**: 36% MCQ miss rate across 563 attempts. Review Rotational Kinematics with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 5.3: Torque**: 36% MCQ miss rate across 410 attempts. Review Torque with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 5.5: Rotational Equilibrium and Newton's First Law in Rotational Form**: 35% MCQ miss rate across 307 attempts. Review Rotational Equilibrium and Newton's First Law in Rotational Form with attention to how the concept appears in AP-style source and evidence questions.

## Review Notes

### Topic 5.1: Rotational Kinematics

A rigid body rotating about a fixed axis is described by angular displacement delta-theta (in radians), angular velocity omega = d-theta/dt, and angular acceleration alpha = d-omega/dt. For constant alpha, the same four kinematic equations from linear motion apply with theta, omega, and alpha replacing x, v, and a. Graphs of theta(t), omega(t), and alpha(t) follow the same slope-and-area logic as their linear counterparts.

- **Angular displacement delta-theta**: Angle in radians through which a rigid body rotates; delta-theta = theta - theta_0. Counterclockwise is typically positive.
- **Angular velocity omega**: omega = d-theta/dt in rad/s; instantaneous rate of change of angular position.
- **Angular acceleration alpha**: alpha = d-omega/dt in rad/s^2; for constant alpha, omega = omega_0 + alpha*t and theta = theta_0 + omega_0*t + (1/2)*alpha*t^2.
- **Rigid body**: A system that holds its shape during rotation; different points move in different directions but the body cannot be modeled as a single point object.
- **Graph interpretation**: The slope of a theta(t) graph gives omega; the slope of an omega(t) graph gives alpha; the area under an alpha(t) graph gives the change in omega.

**Checkpoint:** Write the four constant-alpha kinematic equations from memory, then identify which graph relationship gives you alpha from an omega(t) plot.

Linear quantity | Symbol | Rotational analog | Symbol
--- | --- | --- | ---
Displacement | x | Angular displacement | theta
Velocity | v | Angular velocity | omega
Acceleration | a | Angular acceleration | alpha
Mass | m | Rotational inertia | I
Force | F | Torque | tau

### Topic 5.2: Connecting Linear and Rotational Motion

For any point at distance r from a fixed axis, the arc length is s = r*theta, the tangential speed is v = r*omega, and the tangential acceleration is a_T = r*alpha. All points on a rigid body share the same omega and alpha, but their linear speeds scale with r. The centripetal (radial) acceleration at that point is a_r = r*omega^2, directed toward the axis.

- **s = r*theta**: Arc length traveled by a point at radius r when the body rotates through angle theta (in radians).
- **v = r*omega**: Tangential speed of a point at radius r; points farther from the axis move faster even though omega is the same for all points.
- **a_T = r*alpha**: Tangential component of linear acceleration; changes the speed of the point along its circular path.
- **a_r = r*omega^2**: Centripetal (radial) acceleration directed toward the axis; does not change the point's speed, only its direction.
- **No-slip condition**: For rolling without slipping, v_cm = R*omega and a_cm = R*alpha, linking the translational and rotational motions of the rolling object.

**Checkpoint:** A disk of radius 0.4 m spins at omega = 5 rad/s. Find the tangential speed and centripetal acceleration of a point on the rim.

### Topic 5.3: Torque

Torque is the rotational effect of a force. Only the component of force perpendicular to the position vector from the axis to the point of application produces torque. The magnitude is tau = r*F*sin-theta, where theta is the angle between r and F. The lever arm is the perpendicular distance from the axis to the line of action of the force, giving the equivalent form tau = F * (lever arm). Direction follows the right-hand rule from the cross product tau = r x F.

- **tau = r x F**: Torque as a cross product; magnitude is rF sin-theta, direction is perpendicular to both r and F by the right-hand rule.
- **Lever arm**: Perpendicular distance from the axis of rotation to the line of action of the force; maximizing the lever arm maximizes torque for a given force.
- **Perpendicular force component**: Only F_perp (the component of force perpendicular to r) contributes to torque; the radial component along r produces zero torque.
- **Sign convention**: Counterclockwise torques are typically positive and clockwise torques negative; consistency within a problem is required.
- **Force diagram**: Like a free-body diagram but also shows where each force is applied relative to the axis, which is essential for calculating each torque.

**Checkpoint:** A 10 N force is applied at 0.5 m from a pivot at 30 degrees from the radial direction. Calculate the torque and identify whether it is clockwise or counterclockwise.

### Topic 5.4: Rotational Inertia

Rotational inertia I measures a rigid system's resistance to changes in rotation. It depends on both total mass and how that mass is distributed relative to the axis. For a point mass, I = mr^2. For a collection of point masses, I_total = sum(m_i * r_i^2). For a continuous solid, I = integral r^2 dm, where r is the perpendicular distance from each mass element to the axis. The parallel axis theorem I' = I_cm + Md^2 shifts the axis from the center of mass to any parallel axis a distance d away.

- **I = mr^2**: Rotational inertia of a single point mass m at perpendicular distance r from the axis.
- **I = integral r^2 dm**: Calculus-based formula for continuous solids; requires expressing dm in terms of a spatial variable (dx, dr, etc.) using the object's geometry and density.
- **Parallel axis theorem**: I' = I_cm + Md^2; rotational inertia about any axis equals I about the parallel center-of-mass axis plus Md^2, where d is the distance between the axes.
- **Mass distribution**: Mass farther from the axis contributes more to I (scales as r^2); a hollow cylinder has greater I than a solid disk of the same mass and radius.
- **Common results**: Solid disk: I = (1/2)MR^2; thin cylindrical shell: I = MR^2; thin rod about center: I = (1/12)ML^2; thin rod about end: I = (1/3)ML^2.

**Checkpoint:** Derive the rotational inertia of a uniform thin rod of mass M and length L about one end using I = integral r^2 dm, then verify with the parallel axis theorem from the center result.

Object | Axis | I
--- | --- | ---
Point mass | Distance r from mass | mr^2
Solid disk | Through center, perpendicular | (1/2)MR^2
Thin cylindrical shell | Through center, perpendicular | MR^2
Thin rod | Through center, perpendicular | (1/12)ML^2
Thin rod | Through one end, perpendicular | (1/3)ML^2

### Topic 5.5: Rotational Equilibrium and Newton's First Law in Rotational Form

A system is in rotational equilibrium when the net torque about any chosen axis is zero (sum-tau = 0), which means its angular velocity is constant. This is the rotational analog of Newton's first law. A system can be in rotational equilibrium without being in translational equilibrium, and vice versa. When solving equilibrium problems, choose the pivot point strategically to eliminate unknown torques from the equation.

- **sum-tau = 0**: Condition for rotational equilibrium; the angular velocity is constant (including zero) when net torque is zero.
- **Independent equilibrium conditions**: Rotational equilibrium (sum-tau = 0) and translational equilibrium (sum-F = 0) are separate conditions; a system can satisfy one without the other.
- **Pivot selection**: Any point can serve as the pivot for a torque sum; choosing a point where an unknown force acts eliminates that force from the torque equation.
- **Torque due to gravity**: For a uniform object, gravity acts at the center of mass; the torque from gravity equals Mg times the horizontal distance from the pivot to the center of mass.
- **Unbalanced torque**: If sum-tau is not zero, angular velocity must be changing; the system is not in rotational equilibrium and alpha is nonzero.

**Checkpoint:** A uniform 2 m beam of mass 10 kg is hinged at one end and held horizontal by a vertical rope at the other end. Find the rope tension and hinge force using both sum-F = 0 and sum-tau = 0.

### Topic 5.6: Newton's Second Law in Rotational Form

When net torque on a rigid system is not zero, the system has angular acceleration given by alpha = sum-tau / I_sys, the rotational form of Newton's second law. This is the direct analog of F = ma. For systems that both translate and rotate (such as a mass hanging from a string wrapped around a pulley), you must write a separate sum-F = ma equation for the translational motion and a separate sum-tau = I*alpha equation for the rotational motion, then connect them with a constraint equation such as a = alpha*R.

- **sum-tau = I*alpha**: Newton's second law in rotational form; net torque equals rotational inertia times angular acceleration, directly analogous to F = ma.
- **Combined analysis**: For a pulley-mass system, write sum-F = ma for the hanging mass and sum-tau = I*alpha for the pulley, then use a = alpha*R to solve the system.
- **Constraint equation**: A kinematic relationship linking linear and angular motion, such as a_cm = alpha*R for rolling or a = alpha*R for a string on a pulley, reducing unknowns.
- **Direction consistency**: Choose a positive direction for both linear and rotational motion at the start and apply it consistently across all equations in a combined problem.
- **Rotational inertia in dynamics**: A larger I means a smaller alpha for the same net torque; mass distribution determines how quickly a system responds to an applied torque.

**Checkpoint:** A disk of mass M and radius R has a string wrapped around it with a hanging mass m. Write and solve the system of equations to find the angular acceleration of the disk.

## Study Guides

- [5.1 Rotation](/ap-physics-c-mechanics/unit-5/1-rotation/study-guide/0tVqvv29lj9DIxVt)
- [5.2 Connecting Linear and Rotational Motion](/ap-physics-c-mechanics/unit-5/2-connecting-linear-and-rotational-motion/study-guide/79Ym6NXzWOJH6ZWx)
- [5.3 Torque](/ap-physics-c-mechanics/unit-5/3-torque/study-guide/kQhoEJrKtYjpul5K)
- [5.4 Rotational Inertia](/ap-physics-c-mechanics/unit-5/4-rotational-inertia/study-guide/lSrDkHqB6EviD5CA)
- [5.5 Rotational Equilibrium and Newton's First Law in Rotational Form](/ap-physics-c-mechanics/unit-5/5-rotational-equilibrium-and-newtons-first-law-in-rotational-form/study-guide/hkkIAh5Csy8T6d0p)
- [5.6 Newton's Second Law in Rotational Form](/ap-physics-c-mechanics/unit-5/6-newtons-second-law-in-rotational-form/study-guide/VuXCF8dn0RYwBEaK)

## Practice Preview

### Multiple-choice practice

- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | System A is a point mass $$M$$ attached to a massless rod of length $$R$$. System B is a uniform thin ring of mass $$M$$ and radius $$R$$ rotating about an axis perpendicular to the ring at its edge. Which claim correctly compares their rotational inertias?
- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | A cylinder of mass $$M$$ and radius $$R$$ is pulled by a horizontal force $$F$$ applied at its center of mass. The cylinder rolls without slipping on a rough horizontal surface. Which claim correctly identifies the direction of the friction force $$f$$ exerted by the surface?
- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | A rigid rod of length $$L$$ and mass $$M$$ is pivoted at one end. The rod's linear mass density $$\lambda(x)$$ increases with distance $$x$$ from the pivot. The rod is released from rest in a horizontal position. Which claim correctly compares its initial angular acceleration $$\alpha$$ to that of a uniform rod of the same mass and length?
- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | A flywheel with rotational inertia $$I$$ is initially at rest. Starting at time $$t=0$$, a net torque given by $$\tau(t) = \beta t^2$$ is applied to the flywheel, where $$\beta$$ is a constant. Which expression justifies the angular velocity $$\omega(t)$$ of the flywheel?
- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | Two blocks of mass $$m_1$$ and $$m_2$$ ($$m_1 > m_2$$) are connected by a light string passing over a pulley of radius $$R$$ and rotational inertia $$I$$. The string does not slip. Which claim correctly describes the relationship between the tension $$T_1$$ pulling $$m_1$$ and the tension $$T_2$$ pulling $$m_2$$?
- **AP-style practice question**: Practice 3: Scientific Questioning and Argumentation | A solid sphere and a hollow sphere of equal mass $$M$$ and radius $$R$$ are released from rest at the top of an incline. Both roll without slipping. Which claim correctly identifies the sphere with the greater linear acceleration $$a$$ and provides the valid justification?

### FRQ practice

- **Rotating disk with falling mass and string tension**: FRQ 1 – Mathematical Routines | Rotating disk with falling mass and string tension
- **Rotating disk with hanging masses and string tension**: FRQ 4 – Qualitative/Quantitative Translation | Rotating disk with hanging masses and string tension
- **Rotational dynamics of disk-block system**: FRQ 2 – Translation Between Representations | Rotational dynamics of disk-block system

## Key Terms

- **angular displacement**: The angle in radians through which a rigid body rotates about a specified axis, calculated as delta-theta = theta - theta_0.
- **radian**: The standard unit of angular measurement in rotational kinematics; arc length equals radius times angle in radians.
- **tangential acceleration**: The component of linear acceleration directed tangent to the circular path of a point on a rotating body; a_T = r*alpha.
- **lever arm**: The perpendicular distance from the axis of rotation to the line of action of an applied force; multiplying force by lever arm gives torque magnitude.
- **Moment arm**: The perpendicular distance from the axis of rotation to the line of action of a force; equivalent to lever arm and used interchangeably in torque calculations.
- **cross product**: The vector operation tau = r x F that defines torque; its magnitude is rF sin-theta and its direction is perpendicular to both r and F by the right-hand rule.
- **position vector**: The vector r from the axis of rotation to the point where a force is applied; its magnitude and the angle it makes with the force determine the torque.
- **mass distribution**: The spatial arrangement of mass relative to the axis of rotation; mass farther from the axis contributes more to rotational inertia because I scales as r^2.
- **non-uniform mass distribution**: A mass distribution where density varies with position; requires I = integral r^2 dm with a position-dependent expression for dm.
- **translational equilibrium**: The condition sum-F = 0; independent of rotational equilibrium and must be checked separately in static problems.
- **rolling motion**: Combined translational and rotational motion where the contact point has zero velocity; governed by the no-slip constraint v_cm = R*omega.
- **no-slip condition**: The constraint that the contact point between a rolling object and a surface has zero relative velocity, giving v_cm = R*omega and a_cm = R*alpha.
- **constraint equation**: A kinematic relationship linking linear and angular motion, such as a = alpha*R for a string on a pulley, used to connect the translational and rotational equations in a combined problem.

## Common Mistakes

- **Confusing angular and linear quantities**: Omega and alpha describe the whole rigid body; v and a_T describe a specific point at radius r. Plugging omega directly into a linear equation without multiplying by r is one of the most frequent errors in Unit 5 problems.
- **Using the wrong component of force for torque**: Only the force component perpendicular to the position vector r produces torque. If a force is applied at an angle, you must use F*sin-theta (or equivalently the lever arm), not the full magnitude of F.
- **Forgetting to apply the parallel axis theorem correctly**: I' = I_cm + Md^2 requires I_cm, the rotational inertia about the center of mass, not about some other convenient axis. Using the wrong base value of I leads to an incorrect result.
- **Treating rotational and translational equilibrium as the same condition**: Sum-F = 0 and sum-tau = 0 are independent equations. A beam can have zero net torque but a nonzero net force (or vice versa). Both conditions must be checked separately in static equilibrium problems.
- **Inconsistent sign conventions in combined problems**: In a pulley-mass system, if you define downward as positive for the hanging mass, you must define the corresponding rotation direction as positive for the pulley. Mixing sign conventions across the two equations produces incorrect constraint equations.

## Exam Connections

- **Combined translational and rotational analysis**: AP Physics C: Mechanics frequently presents systems where a mass accelerates linearly while a pulley or spool rotates. You are expected to write separate sum-F = ma and sum-tau = I*alpha equations, identify the correct rotational inertia, and apply a constraint equation to solve for angular acceleration, linear acceleration, or tension. Showing each equation separately before substituting is important for earning full credit.
- **Calculus-based rotational inertia derivations**: Free-response questions may ask you to derive I for a rod of uniform or nonuniform density, a disk, or an annular ring using I = integral r^2 dm. You are expected to set up the integral explicitly, express dm in terms of a spatial variable and the object's geometry, evaluate the integral, and apply the parallel axis theorem if the axis is not through the center of mass.
- **Rotational equilibrium with force and torque diagrams**: Problems involving beams, hinges, or suspended rods require both a force diagram and a torque equation. You are expected to choose a pivot strategically, correctly identify each torque's sign and lever arm, and recognize that satisfying sum-tau = 0 does not automatically satisfy sum-F = 0. Justifying your pivot choice and showing the torque sum explicitly are standard expectations.

## Final Review Checklist

- **Final Unit 5 review checklist**: Use this list to confirm you can handle every major skill in Unit 5 before the exam.
- **Write and apply the constant-alpha kinematic equations**: Given initial angular velocity, angular acceleration, and time (or angle), solve for any unknown using omega = omega_0 + alpha*t, theta = theta_0 + omega_0*t + (1/2)*alpha*t^2, and omega^2 = omega_0^2 + 2*alpha*(delta-theta).
- **Convert between angular and linear quantities**: Use s = r*theta, v = r*omega, and a_T = r*alpha to find the linear motion of a specific point on a rotating rigid body given its distance from the axis.
- **Calculate torque using the cross product and lever arm**: Find tau = rF sin-theta for a force applied at angle theta from the radial direction, or equivalently multiply the force by its lever arm. Assign correct sign based on clockwise or counterclockwise direction.
- **Derive rotational inertia using integration and the parallel axis theorem**: Set up I = integral r^2 dm for uniform and nonuniform rods, disks, cylindrical shells, and annular rings. Apply I' = I_cm + Md^2 to shift the axis off the center of mass.
- **Apply rotational equilibrium (sum-tau = 0)**: Choose a pivot strategically, write the torque equation, and solve for unknown forces or distances. Recognize that rotational equilibrium does not require translational equilibrium.
- **Solve combined translational and rotational dynamics problems**: Write sum-F = ma for linear motion and sum-tau = I*alpha for rotation, then use a constraint equation (a = alpha*R or v_cm = omega*R) to connect the two equations and solve for unknowns.

## Study Plan

- **Step 1: Rotational kinematics and the linear connection (Topics 5.1-5.2)**: Read the Topic 5.1 and 5.2 guides. Practice writing the constant-alpha equations from memory and converting between angular and linear quantities using s = r*theta, v = r*omega, and a_T = r*alpha. Sketch theta(t) and omega(t) graphs and identify slopes and areas.
- **Step 2: Torque (Topic 5.3)**: Read the Topic 5.3 guide. Practice drawing force diagrams that show where each force is applied relative to the axis. Calculate torques using both tau = rF sin-theta and the lever arm method. Apply the right-hand rule to determine direction.
- **Step 3: Rotational inertia (Topic 5.4)**: Read the Topic 5.4 guide. Derive I for a uniform rod about its end and about its center using integration, then verify the end result with the parallel axis theorem. Memorize the standard results for disks and cylindrical shells. Practice setting up dm in terms of a spatial variable for nonuniform rods.
- **Step 4: Rotational equilibrium (Topic 5.5)**: Read the Topic 5.5 guide. Solve beam and lever problems by writing sum-tau = 0 about a strategically chosen pivot. Practice identifying which forces produce zero torque about a given pivot and why.
- **Step 5: Newton's second law in rotational form and combined systems (Topic 5.6)**: Read the Topic 5.6 guide. Set up and solve pulley-mass and rolling-object problems by writing separate sum-F = ma and sum-tau = I*alpha equations, then connecting them with a constraint equation. Use the AP score calculator to estimate your overall score as you complete practice problems.

## More Ways To Review

- [Topic study guides](/ap-physics-c-mechanics/unit-5#topics)
- [Practice questions](/ap-physics-c-mechanics/guided-practice?unitSlug=unit-5)
- [FRQ practice](/ap-physics-c-mechanics/frq-practice)
- [Key terms](/ap-physics-c-mechanics/key-terms)

## FAQs

### What topics are covered in AP Physics Mech Unit 5?

AP Physics C: Mechanics Unit 5 covers 6 topics: Rotational Kinematics, Connecting Linear and Rotational Motion, Torque, Rotational Inertia, Rotational Equilibrium and Newton's First Law in Rotational Form, and Newton's Second Law in Rotational Form. Together they build the rotational counterparts to the linear dynamics you studied earlier in the course. See the full topic breakdown at [AP Physics C: Mechanics Unit 5](/ap-physics-c-mechanics/unit-5).

### How much of the AP Physics Mech exam is Unit 5?

Unit 5 makes up 10-15% of the AP Physics C: Mechanics exam. That weight covers Torque and Rotational Dynamics, including Rotational Kinematics, Torque, Rotational Inertia, Rotational Equilibrium, and Newton's Second Law in Rotational Form. It's a meaningful chunk of the exam, so strong fluency with these concepts pays off on both the MCQ and FRQ sections.

### What's on the AP Physics Mech Unit 5 progress check (MCQ and FRQ)?

The AP Physics C: Mechanics Unit 5 progress check in AP Classroom includes both MCQ and FRQ parts drawn from all six unit topics: Rotational Kinematics, Connecting Linear and Rotational Motion, Torque, Rotational Inertia, Rotational Equilibrium, and Newton's Second Law in Rotational Form. The MCQ part tests conceptual understanding and calculation, while the FRQ part typically asks you to derive expressions, apply Newton's Second Law in rotational form, or analyze rotational equilibrium scenarios. For matched practice before the progress check, visit [AP Physics C: Mechanics Unit 5](/ap-physics-c-mechanics/unit-5).

### How do I practice AP Physics Mech Unit 5 FRQs?

The best way to practice Unit 5 FRQs is to work through problems that mirror the three most common question types: deriving rotational inertia expressions, applying Newton's Second Law in rotational form to systems with torque, and analyzing rotational equilibrium. These topics, especially 5.4 Rotational Inertia and 5.6 Newton's Second Law in Rotational Form, show up most often in free-response questions on the AP Physics C: Mechanics exam. Start by writing out full solutions with clear diagrams and labeled torque directions, then check your reasoning step by step. You'll find FRQ-aligned practice at [AP Physics C: Mechanics Unit 5](/ap-physics-c-mechanics/unit-5).

### Where can I find AP Physics Mech Unit 5 practice questions?

For AP Physics C: Mechanics Unit 5 practice questions, including multiple-choice and practice test problems on Torque and Rotational Dynamics, head to [AP Physics C: Mechanics Unit 5](/ap-physics-c-mechanics/unit-5). You'll find MCQ-style questions covering Rotational Kinematics, Torque, Rotational Inertia, and Newton's Second Law in Rotational Form, plus FRQ practice that mirrors what College Board tests on the actual exam.

### How should I study AP Physics Mech Unit 5?

Start with Rotational Kinematics (5.1) and Connecting Linear and Rotational Motion (5.2) to build the foundation, since every later topic depends on those analogies between linear and rotational quantities. Then work through Torque (5.3) and Rotational Inertia (5.4) together, practicing the integral definitions of inertia for common shapes. Once those feel solid, tackle Rotational Equilibrium (5.5) and Newton's Second Law in Rotational Form (5.6) with full free-body and torque diagrams on every problem. A few concrete steps that help: draw the rotational analog table (x vs. theta, v vs. omega, F vs. tau) and keep it visible while you practice. Do at least one FRQ per topic from past exams, writing out every step rather than just checking the answer. Visit [AP Physics C: Mechanics Unit 5](/ap-physics-c-mechanics/unit-5) for organized practice by topic.

## Structured Data

```json
{"@context":"https://schema.org","@type":"FAQPage","inLanguage":"en","mainEntity":[{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-mechanics/unit-5#what-topics-are-covered-in-ap-physics-mech-unit-5","name":"What topics are covered in AP Physics Mech Unit 5?","acceptedAnswer":{"@type":"Answer","text":"AP Physics C: Mechanics Unit 5 covers 6 topics: Rotational Kinematics, Connecting Linear and Rotational Motion, Torque, Rotational Inertia, Rotational Equilibrium and Newton's First Law in Rotational Form, and Newton's Second Law in Rotational Form. Together they build the rotational counterparts to the linear dynamics you studied earlier in the course. See the full topic breakdown at <a href=\"/ap-physics-c-mechanics/unit-5\">AP Physics C: Mechanics Unit 5</a>."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-mechanics/unit-5#how-much-of-the-ap-physics-mech-exam-is-unit-5","name":"How much of the AP Physics Mech exam is Unit 5?","acceptedAnswer":{"@type":"Answer","text":"Unit 5 makes up 10-15% of the AP Physics C: Mechanics exam. That weight covers Torque and Rotational Dynamics, including Rotational Kinematics, Torque, Rotational Inertia, Rotational Equilibrium, and Newton's Second Law in Rotational Form. It's a meaningful chunk of the exam, so strong fluency with these concepts pays off on both the MCQ and FRQ sections."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-mechanics/unit-5#whats-on-the-ap-physics-mech-unit-5-progress-check-mcq-and-frq","name":"What's on the AP Physics Mech Unit 5 progress check (MCQ and FRQ)?","acceptedAnswer":{"@type":"Answer","text":"The AP Physics C: Mechanics Unit 5 progress check in AP Classroom includes both MCQ and FRQ parts drawn from all six unit topics: Rotational Kinematics, Connecting Linear and Rotational Motion, Torque, Rotational Inertia, Rotational Equilibrium, and Newton's Second Law in Rotational Form. The MCQ part tests conceptual understanding and calculation, while the FRQ part typically asks you to derive expressions, apply Newton's Second Law in rotational form, or analyze rotational equilibrium scenarios. For matched practice before the progress check, visit <a href=\"/ap-physics-c-mechanics/unit-5\">AP Physics C: Mechanics Unit 5</a>."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-mechanics/unit-5#how-do-i-practice-ap-physics-mech-unit-5-frqs","name":"How do I practice AP Physics Mech Unit 5 FRQs?","acceptedAnswer":{"@type":"Answer","text":"The best way to practice Unit 5 FRQs is to work through problems that mirror the three most common question types: deriving rotational inertia expressions, applying Newton's Second Law in rotational form to systems with torque, and analyzing rotational equilibrium. These topics, especially 5.4 Rotational Inertia and 5.6 Newton's Second Law in Rotational Form, show up most often in free-response questions on the AP Physics C: Mechanics exam. Start by writing out full solutions with clear diagrams and labeled torque directions, then check your reasoning step by step. You'll find FRQ-aligned practice at <a href=\"/ap-physics-c-mechanics/unit-5\">AP Physics C: Mechanics Unit 5</a>."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-mechanics/unit-5#where-can-i-find-ap-physics-mech-unit-5-practice-questions","name":"Where can I find AP Physics Mech Unit 5 practice questions?","acceptedAnswer":{"@type":"Answer","text":"For AP Physics C: Mechanics Unit 5 practice questions, including multiple-choice and practice test problems on Torque and Rotational Dynamics, head to <a href=\"/ap-physics-c-mechanics/unit-5\">AP Physics C: Mechanics Unit 5</a>. You'll find MCQ-style questions covering Rotational Kinematics, Torque, Rotational Inertia, and Newton's Second Law in Rotational Form, plus FRQ practice that mirrors what College Board tests on the actual exam."}},{"@type":"Question","@id":"https://fiveable.me/ap-physics-c-mechanics/unit-5#how-should-i-study-ap-physics-mech-unit-5","name":"How should I study AP Physics Mech Unit 5?","acceptedAnswer":{"@type":"Answer","text":"Start with Rotational Kinematics (5.1) and Connecting Linear and Rotational Motion (5.2) to build the foundation, since every later topic depends on those analogies between linear and rotational quantities. Then work through Torque (5.3) and Rotational Inertia (5.4) together, practicing the integral definitions of inertia for common shapes. Once those feel solid, tackle Rotational Equilibrium (5.5) and Newton's Second Law in Rotational Form (5.6) with full free-body and torque diagrams on every problem. A few concrete steps that help: draw the rotational analog table (x vs. theta, v vs. omega, F vs. tau) and keep it visible while you practice. Do at least one FRQ per topic from past exams, writing out every step rather than just checking the answer. Visit <a href=\"/ap-physics-c-mechanics/unit-5\">AP Physics C: Mechanics Unit 5</a> for organized practice by topic."}}]}
```