AP Physics C: Mechanics

We will complete a Kinematics Overview, in which we will explore dynamics and movement, as well as the necessary equations needed for the Kinematics Unit! We will be asking (and answering!) why objects move the way they do (using algebra and calculus!) and how to calculate an object's speed, distance, and rate of change of speed!

AP Mechanics Kinematics Overview

Join us for a fun and fresh overview of AP Physics C Mechanics! We will go over the 7 units, and collaboratively work on a simple practice FRQ to get a feel for what the questions will be like!

Course Overview + Unit 1 Review + FRQ Practice

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AP Physics C: Mechanics Courses Open House

One of the most common applications of gravitation that AP enjoys is the orbits of planets and satellites!

Fast Facts of Planets and Satellites in Orbit:

This also means that the kinetic energy of a satellite in orbit can be simplified down to only be dependent on the satellite and its distance.

The centripetal force acting on a satellite/planet system is caused by the gravitational force.

This means that we can derive some formulas to describe the orbits of these systems that move in a circular path.

Additionally, I'll leave the proof of this one as an exercise for you, but we can use a similar method to determine the 

There is another version of this formula which is known as 

 which is only applicable for objects in circular orbit:

This is commonly rewritten as below in order to simplify the relationship:

 situations in relation to satellites, you can use the conservation of energy in order to help you describe its motion. 

Most Physics C: Mechanics classes tend to skip over Kepler's Laws, so note that it is perfectly acceptable to justify your answer with other physics you know.

Orbits of Planets and Satellites

Gravitation may be the last and shortest unit, but you can see the applications of everything you've learned so far in this unit! From momentum to energy to forces, everything has accumulated to this point.

Unit 5 will cover approximately 6%-14% of the exam and should take around 5 to 10, 45-minute class periods to cover. The 

 personal progress check has 10 multiple choice questions and 1 free response question for you to practice on.

When an object is large enough/massive enough it will create its own gravitational field which can interact with other objects that have gravitational fields.

: Every object attracts every other object in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance/radius between their centers.

You can see the equation form of the law below:

 is the distance between the two masses, and 

Essentially, this law is an extension of Newton's Third Law in which every action has an equal and opposite reaction.

Here's a diagram that illustrates the law:

Now, we can use this equation to find the acceleration due to gravity on an object!

g is the acceleration due to gravity and we can cancel out the mass, therefore:

if the object is far from the earth's surface, we use the distance from the earth to the object rather than the earth's radius:

Additionally, it should be noted that gravity is a 

, meaning that its path is independent of it and the total work on a closed path is zero. Note that work done by a conservative force is equal to the negative change in potential energy. However, it is not 

This might be intuitive to some, but the further away the object is, the weaker the gravitational force acting on it from the other object will be. You can see this below:

Gravitational Forces

 is the rotational analog of force, which is what causes an object to rotate around its center of mass. It's units are (kg

 of the radius(r) and the force(F) applied at that radius, which in equation form is:


Here's an image of an application of torque:

 This condition is about static and dynamic equilibrium in which the object either has a 0 or constant velocity and the acceleration is 0, meaning the net force is zero. 

This condition states that the sum of the net torques is 0 and the angular acceleration is 0.

Both of these conditions must be satisfied in order for an object/system to be in equilibrium!

 or Moment of Inertia is essentially an object's resistance to changes in its rotation. It is essentially the sum of all the tiny points of mass times the radius(r) squared of an object, in which the calculus definition for it is:

However, these derivations typically take a very long time and require a strong level of comfort in calculus, so AP doesn't usually make students derive them. Most of the time they will use one that is very common, like a rod, or they will give it to you in the question.

Here are some examples of the most commonly seen ones, take a look at the axis of rotation too!

Sometimes, the axis of rotation isn't perfectly where we want it to be: at the center of mass. So we employ an awesome trick called 

In which I(new) is the rotational inertia of the object with the shifted axis, I(com) is the rotational inertia of the object with the axis at the center of mass (like the image above), m is mass, and h is the shift of the axis in meters.

1) Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible. (

Torque and Rotational Statics 🔧

Objects can move rotationally and translationally! So we need to find ways to describe both.
Δ𝛳 is the change in the angular position, in radians, and is the rotational analog for displacement Δx 
ѡ is angular velocity in the units radians per second, and is the rotational analog for velocity(v).
ɑ is angular acceleration in the units of radians per second squared and is the rotational analog for acceleration(a).

You may notice that there's no such thing as angular time here, which is great for us as its one of the ways we can tie these two worlds together with something other than radius!

Below we can see the comparisons between translational and rotational motion, and you may notice things are eerily similar.


The formulas that work for both, other than the last one, require the object to be 

, which essentially means that there is a torque on the object. For example, look at the picture below:


1) Large freight trains accelerate very slowly. Suppose one such train accelerates from rest, giving its 0.350-m-radius wheels an angular acceleration of 0.250 rad/s2. After the wheels have made 200 revolutions (assume no slippage): (a) How far has the train moved down the track? (b) What are the final angular velocity of the wheels and the linear velocity of the train? ([Taken from Lumen Learning)]

Remember the equation between theta and radius:
Δx=r𝛳


Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled.

(a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s^2, what is the angular acceleration of the yo-yo?(b) What is the angular velocity after 0.750 s if it starts from rest? 

Rotational Kinematics 💿

Unit 4: Systems of Particles and Linear Momentum 

Momentum, like energy, is a concept that can be easily applied in most physics scenarios, even when it isn't conserved. Momentum is easy to use to connect different units because it can be used to describe basically any system of objects in motion. 

Unit 4 will cover approximately 14%-17% of the exam and should take around 10 to 20, 45-minute class periods to cover. The 

 personal progress check has 15 multiple choice questions and 1 free response question for you to practice on. 

AP Physics C Mechanics Exam Prep 2020-21

browse by unit

Free Reviews

Unit 1: Kinematics

Unit 2: Newton's Laws of Motion

Unit 3: Work, Energy, and Power

Unit 4: Systems of Particles and Linear Momentum

Unit 5: Rotation

Unit 6: Oscillations

Unit 7: Gravitation

Blogs

creators

Riya Patel

Gerardo Rafael Bote

Daniella Garcia-Loos

Kristen Adams

AP Physics C Mechanics Exam Prep 2020-21

browse by unit

Free Reviews﻿

Unit 1: Kinematics﻿

Unit 2: Newton's Laws of Motion﻿

Unit 3: Work, Energy, and Power﻿

Unit 4: Systems of Particles and Linear Momentum﻿

Unit 5: Rotation﻿

Unit 6: Oscillations﻿

Unit 7: Gravitation ﻿

Blogs﻿

creators

Riya Patel﻿

Gerardo Rafael Bote﻿

Daniella Garcia-Loos﻿

Kristen Adams﻿

Free Reviews

Unit 1: Kinematics

Unit 2: Newton's Laws of Motion

Unit 3: Work, Energy, and Power

Unit 4: Systems of Particles and Linear Momentum

Unit 5: Rotation

Unit 6: Oscillations

Unit 7: Gravitation

Blogs

Riya Patel

Gerardo Rafael Bote

Daniella Garcia-Loos

Kristen Adams