AP Physics 1 : Angular Momentum

Study concepts, example questions & explanations for AP Physics 1

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Example Questions

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Example Question #1021 : Ap Physics 1

Two cars are racing side by side on a perfectly circular race track. The inner car is from the center of the track. The outer car is from center of the track.

If the outer car is moving at , determine it's angular momentum.

Possible Answers:

Correct answer:

Explanation:

Example Question #1022 : Ap Physics 1

Moment of inertia of disk:

A car with wheels of mass and wheels of radius is traveling at . Treating the wheels as disks of uniform mass density, calculate the angular momentum of one wheel.

Possible Answers:

None of these

Correct answer:

Explanation:

Finding angular velocity:

Using

and

Where is angular momentum

Combining equations and plugging in values:

Example Question #1023 : Ap Physics 1

A solid bowling ball of mass  and radius  is traveling at a linear velocity of . What is the angular momentum of the ball?

Possible Answers:

Correct answer:

Explanation:

The expression for angular momentum is:

Where I is the moment of inertia for a solid sphere:

And w is the angular velocity:

Plugging these in, we get:

Plugging in our values, we get:

Example Question #11 : Angular Momentum

A bowling ball of mass  and radius  is traveling down a slope with a vertical height change of . If the ball starts from rest, what is the final linear velocity of the ball as it reaches the bottom of the slope? Neglect air resistance.

Possible Answers:

Correct answer:

Explanation:

Let's begin with the expression for conservation of energy:

Since the ball begins from rest, we can eliminate initial kinetic energy. Also, if we assume that the bottom of the slope has a height of 0, we can eliminate final potential energy to get:

Plugging in expressions, we get:

Where I is the moment of inertia for a solid sphere:

And w is the angular velocity:

Plugging these in, we get:

Rearranging for final velocity, we get:

Plugging in our values, we get:

Example Question #31 : Circular And Rotational Motion

Two identical cars are racing side by side on a circular race track. Which has the greater angular momentum?

Possible Answers:

They are the same

The outside car

Impossible to determine

The inside car

Correct answer:

The outside car

Explanation:

Where  is the radius of the circle

 is the mass of the object 

 is the linear velocity of the object

The car on the outside has a larger  and a larger , and the same , thus it has a higher angular momentum.

Example Question #11 : Angular Momentum

 weight on a  rope is swung around at  until it comes into contact with a resting  brick on flat ground. The brick travels . What is the coefficient of kinetic friction between the the brick and ground?

Possible Answers:

Correct answer:

Explanation:

The first part of this problem is a transfer between angular and linear momentum. Conservation of momentum tells us that we can equate the angular momentum of the pendulum to the linear momentum of the brick, or , where  and  are the masses of the pendulum and brick respectively,  is the angular velocity of the pendulum in  is the length of the pendulum rope, and  is the resultant velocity of the brick. We find that the resulting velocity of the brick can be written as 

The next part of the problem is identifying that the kinematic equations can be used here to find the acceleration the brick undergoes as it comes to a stop. Here we can use , where  is the end velocity of the brick (zero),  is the deceleration it undergoes, and  is the distance the brick travels before coming to a stop. Solving for  we have that .

Lastly, we know that the kinetic friction force can be written as . Newton's second law says that this can be written as . Thus we find that .

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