Rotational Kinetic Energy and Angular Momentum

Rotational Kinetic Energy and Angular Momentum

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Multiple Choice

Two bugs are on a spinning wheel. Which bug has the greater tangential (linear) velocity?

• Bug 1

• Bug 2

• It's the same!

Multiple Choice

Two bugs are on a spinning wheel. Which bug has the greater angular velocity?

• Bug 1

• Bug 2

• It's the same!

Each bug will rotate once in the same amount of time.

Torques CHANGE rotation

• to get something rotating

• or to stop something rotating

• you need a TORQUE

Torque

Fill in the Blanks

The see-saw is balance.d What is the weight of the person hanging off the edge?

Fill in the Blanks

How far from the fulcrum is the boy?

Fill in the Blanks

Johnny McNoFriends balances by himself on the see-saw. What is the weight of the board?

Multiple Choice

The broom balances at its CG. If you cut the broom at the CG and weigh each part of the broom, which end would weigh more?

• Handle end

• Bristle end

• Same!

Multiple Choice

A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown above. A force F is applied at the other end, at an angle θ to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque?

• Lsin $$\theta$$

• Lcos $$\theta$$

• L

• Ltan $$\theta$$

• $$\sqrt{2}$$ L

Rotational Inertia

Rotational Inertia

• More mass = more rotational inertia

• The farther the mass is from the point of rotation = more rotational inertia

Rotational Inertia

Rotational Inertia

Newton's 2nd Law

Rotational Form

Multiple Choice

A given force is applied to a wrench to turn a bolt of specific rotational inertia I which rotates freely about its center as shown in the following diagrams. Which of the following correctly ranks the resulting angular acceleration of the bolt?

• αF >αA =αC >αB =αD >αE

• αC =αF >αA =αB >αD >αE

• αA =αF >αC =αE >αB =αD

• αD =αF >αA =αC >αB >αE

Multiple Choice

A hoop with moment of inertia I=0.1 kg•m² spins about a frictionless axle with an angular velocity of 5 rad/s. At what radius from the center of the hoop should a force of 2 N be applied for 3 s in order to accelerate the hoop to an angular speed of 10 rad/s?

• 8.3 cm

• 12.5 cm

• 16.7 cm

• 25 cm

Rotational Kinetic Energy

Multiple Choice

A cart (mass M) slides across a surface (no friction), with speed v hits an incline. A wheel (mass M and radius R) rolls with speed v without slipping and hits an identical incline. The wheel does not slip as it rolls up the incline. No friction in the bearings in the cart.

Which object goes higher up the incline?

• cart

• wheel

• same

Multiple Choice

A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s moment of inertia about the axis is 4 kg m². At time t = 0 the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second.

What is the kinetic energy of the cylinder at time t = 2 seconds?

• 1 J

• 2 J

• 3 J

• 4 J

• cannot be determined without knowing the radius of the cylinder

Multiple Choice

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane is frictionless, what is the speed v_cm, of the center of mass of the sphere at the bottom of the incline?

• $$\sqrt[]{2gh}$$  

• $$\frac{2Mgh}{I}$$  

• $$\frac{2Mghr^2}{I}$$  

• $$\sqrt[]{\frac{2Mghr^2}{I}}$$  

• $$\sqrt[]{\frac{2Mghr^2}{I\ +\ Mr^2}}$$  

Multiple Choice

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane has friction so that the sphere rolls without slipping, what is the speed v_cm of the center of mass at the bottom of the incline?

• $$\sqrt[]{2gh}$$  

• $$\frac{2Mgh}{I}$$  

• $$\frac{2Mghr^2}{I}$$  

• $$\sqrt[]{\frac{2Mghr^2}{I}}$$  

• $$\sqrt[]{\frac{2Mghr^2}{I\ +\ Mr^2}}$$  

Angular Momentum

Conservation of Angular Momentum

Conservation of Angular Momentum

Multiple Choice

A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s moment of inertia about the axis is 4 kg m². At time t = 0 the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second.

What is the angular momentum of the cylinder at time t = 2 seconds?

• 1 kgm m²/s

• 2 kgm m²/s

• 3 kgm m²/s

• 4 kgm m²/s

• cannot be determined without knowing the radius of the cylinder

Multiple Choice

The diagram shows a top view of a child of mass M on a circular platform of mass 2M that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following describes an action by the child that will increase the angular speed of the platform-child system and gives the correct reason why?

• The child moves toward the center of the platform, increasing the total angular momentum of the system

• The child moves toward the center of the platform, decreasing the rotational inertia of the system.

• The child moves away from the center of the platform, increasing the total angular momentum of the system.

• The child moves away from the center of the platform, decreasing the rotational inertia of the system.

Multiple Choice

A thin rod of length d on a frictionless surface is pivoted about one end, as shown above, and can rotate freely. The rod is at rest when it is struck by a sphere with linear momentum of magnitude p_i perpendicular to the rod. The sphere rebounds along its original line of motion with momentum of magnitude p_f . What is the magnitude of the angular momentum of the rod immediately after the collision?

• p_f  - p_i

• p_f  + p_i

• (p_f  - p_i)d

• (p_f  + p_i)d