It's that time of year again. You're picking courses for next year and you see AP Physics C: Mechanics and AP Physics C: E & M in your course catalog 🤩 You've heard from other students that they're some of the hardest classes offered 🥴, but you aren't really sure how true that is. We're here to help you 🥳

How Difficult is AP Physics C: Mechanics?

AP Physics C: Mechanics is the first of the two AP Physics C courses and deals exclusively with Newtonian mechanics 🍎 Much of the work deals with the motion of various objects and will take the form of long word problems. Many of them will also ask you to draw a free body diagram of the forces on objects ➡️ The multiple-choice will be more conceptual than the long problems but will still contain math for many of the problems as compared to AP Physics 1 and 2.

Free Body Diagrams similar to the type you will draw on your assignments and the AP Test. Image Courtesy of 

AP Physics C: Mechanics is usually the easier of the two AP Physics Cs; however, there are still problems that make you question your existence, especially with complex dynamics and rotational motion questions! Don't let your guard down ✊🏼

You can take other AP classes along with AP Physics C: Mechanics. To be successful, you should go into the course after already taking AP Calculus AB ♾️ as a prerequisite. AP Physics C: Mechanics will be your hardest AP course and should not be taken with any other of the AP sciences (except E & M).

AP Physics C: E & M is the second of the two AP Physics C courses and deals with electricity, magnetism, and the relationship between the two, called electromagnetic induction ⚡ Many problems will explore the concept of field forces (forces that don't necessarily have to touch the object) and will ask you to derive a formula when given a specific scenario.💡 The multiple-choice assignments will be more conceptual than with Mechanics.

A LC circuit, which is one of the types of circuits studied in AP Physics C: E & M. Image Courtesy of 

University of Louisville Physics and Astronomy

AP Physics C: E & M is rightfully the harder of the two AP Physics C courses because of its conceptual nuance and the complex derivations, most of which require integration 😳 This course is done best with a prerequisite or corequisite of AP Calculus BC. This course will require a lot of work to be put into mastering the material, so stay on top of your assignments and studying 💪🏼

Are AP Physics C: Mechanics and E & M Worth Taking?

AP Physics C: Mechanics and AP Physics C: E & M are the first two courses in a calculus-based physics sequence at most universities 🏫 Unlike other AP subjects, these two give college credit most of the time for these two courses and fulfill general education requirements at many schools 🖊️

If you intend to go into a medical field, medical schools are looking for two semesters of calculus-based physics which can be fulfilled by these two courses 🏥

For many STEM majors, these two courses are prerequisites for many other courses, especially in engineering. Mechanics will be a prerequisite for many mechanical and civil engineering classes, such as statics and dynamics. E & M will be a prerequisite for many electrical engineering classes as well as higher topics in physics such as computer architecture and quantum physics.

Due to the versatility of this credit, we think that these two are definitely worth taking 🙌

Yes, AP Physics C: Mechanics and E & M are two of the hardest courses offered in high school, but it's totally worth it! Remember, you're not alone in this—join a Fiveable course today to be part of an inclusive community.  You got this 🎉

Are AP Physics C Courses Hard/Worth Taking?

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. 

Unit 4: Systems of Particles and Linear Momentum

, also sometimes called the center of gravity, is typically what we refer to as the geometric position in an object defined by: 

the mean position of every section of the object or system, weighted by mass

. In other words, this is a place where the object is 

Below you can see an example of finding the center of mass in the x direction of a system of masses:


Another way to format the above formula is with linear mass density:


 is typically a constant for something that is uniform, so it can be found with an equation like:



However, since AP loves to make us do calculus, we will sometimes see non-uniform objects! This means that the linear mass density would be a function. 


Let's try to calculate the center of mass of a uniform rod!

We can begin with one of the formulas we discussed above and place bounds on it:


Since we know that the rod is uniform, we can take the linear mass density out of the integral because it is a constant. 



As you can see, the lambdas cancel out! Now we can evaluate the integrals. 



Now we can plug in our bounds and simplify. This leads us to:



Hopefully, this answer seems intuitive to you! We'll be seeing problems similar to this when we tackle rotational inertia next unit. 



Even though AP Physics 1 is not calculus-based, we can practice applications of the center of mass with FRQs from that test too!

The trick to this question is realizing that it is asking for the 

. So the speed of it should only change when momentum isn't conserved, meaning when there is impulse!

Same focus as before, realize it is the center of mass of the system! Think of how you were searching for the x coordinate of the center of mass, you can apply the same strategy for velocity. 


Center of Mass 🏒

In this unit, we'll only be talking about 

, but look forward to angular momentum in the next unit! Conceptually, its quite hard to describe without using quantities, but essentially, it is a measurement of mass in motion. The most basic equation for 

Let's try to derive Newton's Second Law using momentum!

Now that looks pretty familiar, doesn't it?

Let's take a closer look at one part of this derivation.

This change in momentum actually has a special name, 

We tend to use calculus when the force or the mass is variable, like with a rocket!

 is a vector because force has a direction, and the units are the same as momentum(N*s). Additionally, AP loves to ask questions about impulse in relation to graphs!

Impulse is the area under the curve (check out the integral!) of a Force vs. Time graph.

The curves won't always look this pretty like they did in AP Physics 1 because we have the power of calculus now!

Have you ever tried an egg drop experiment? One where you tried to shield a poor egg from cracking as soon as it hit the ground?

Think back to which experiments worked best...theoretically the ones that work best should be the ones that increase the amount of time of impact!

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (209 km/h). What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?(


To determine the change in momentum, substitute the values for the initial and final velocities into the equation above.



Now the magnitude of the net external force can determined by using 



Use the Impulse formula on your formula chart, and don't forget to include your bounds/limits of integration!



Again, use the formula on your chart and integrate with bounds. Take note that there is an alternate form of resolving this with another impulse formula


Impulse and Momentum 🥚

4.3: Conservation of Linear Momentum and Collisions 🎱

💡 The total momentum, magnitude, and direction are conserved in a system unless acted on by an outside force. 


This law of conservation can also be written as:



The initial momentum is equal to the final momentum, if there was no impulse. 


So...why is momentum conserved in a collision?

We have to blame it on Newton, again! Think back to Newton's Third Law: every action has an equal and opposite reaction. This means that there is an equal and opposite force acting on the two objects that collided.

So let's see if there's an impulse from a collision. Since impulse is equal to the change in momentum, if it is 0, we know that momentum was conserved. The change in momentum of both objects is the same magnitude, but different directions. So the sum of these is zero!

A collision is the most basic application of conservation of momentum, from pool balls knocking each other to a rocket launching, collisions occur daily. They typically involve a 

 interacting with some speed. The forces these masses enact on each other do not affect the conservation of momentum of the system, because there is no net force!

Below is an example of a scenario before and after, where momentum is conserved:

Sometimes referred to as "Bouncy" collisions

If a collision is perfectly inelastic or "sticky", the max amount of kinetic energy is lost 

 a fun interactive cart lab you can mess around with! Check out the different types of collisions and how velocity and mass affect the system. 


(For part 1 you'll need the answer for part a of this question, which is -2.03 N*s)




Impulse is equal to the change in momentum, and in this scenario mass is not changing so we can look at this problem with initial and final velocity. Remember that velocity is a vector, so positives and negatives represent direction!



Use conservation of momentum to calculate the speed of cart 2. Then, you should recall that kinetic energy is conserved in elastic collisions. 


Conservation of Linear Momentum and Collisions 🎱

This unit is allllll about objects that rotate! From a spinning record to a satellite, we can use this unit to describe the motion (or lack of) for these situations. Additionally, we will be making connections between this unit and previous units in ways such as demonstrating the analogs between translational and rotational kinematics.

Unit 5 will cover approximately 14%-20% of the exam and should take around 10 to 20, 45-minute class periods to cover. The

 personal progress check has 20 multiple choice questions and 1 free response question for you to practice on.

Unit 5: Rotation

 This is essentially the rotational analog for Newton's Second Law in which the sum of the net torques is equal to the rotational inertia times the angular acceleration(which should be constant if force is not variable).

This means that the further away from the axis the greater the torque is! In addition to this force analog, we also have an analog for one of the most important parts of a problem in physics: force diagrams/free body diagrams. This analog is most commonly referred to as a 

. It is very similar to an FBD, except you can see where the force is being applied to the diagram! They usually look something like:

A large portion of the time you will have to use force diagrams and equations in conjunction with torque!

As with almost everything else that is translational, there is a form of 

! This does not mean that there isn't any other type of energy occurring though! Most of the time there will be a combination of translational and rotational kinetic energy.


Rotational Dynamics and Energy 🐞

5.4: Angular Momentum and Its Conservation 🛰️

 Angular momentum of a system is conserved unless there is an outside torque acting on the system.


Which means that torque is the slope of an angular momentum vs. time graph!

Common misconception: You cannot just multiply r by translational momentum to change it to angular!!

 L does not equal mvr for anything other than a point/particle!

Common Situations of Conservation of Angular Momentum

This situation is extremely similar to pool ball scenarios we've seen in the past with linear momentum, however, we typically considered those pool balls as a particle/point in space. Disks have some rotational inertia so they can apply torque on each other. However, it is important to remember that angular momentum is conserved because these torques are inside the system!

Here's an example of a disk collision below:

A ballistic pendulum typically refers to a bullet/particle-like object shot at a physical pendulum, like a rod. You can see an example of the scenario below:

Typically it can be solved with a combination of conservation of energy and momentum! When the pendulum has some rotational inertia, we have to use conservation angular momentum for the bullet-pendulum system.

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AP Physics C Mechanics Exam Prep 2020-21⚙️

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Study by Unit

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Unit 2﻿

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Unit 4﻿

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Unit 6﻿

Oscillations﻿

Unit 7﻿

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