AP Unit 5: Rotation

Torque is the rotational analogue of:

• kinetic energy

• linear momentum

• acceleration

• force

• mass

A cylinder, with a moment of inertia ( I = 10 kgm² ), is rotating about a frictionless, fixed pivot with an angular velocity ω = 4t² + 2 . What is the angular displacement of the cylinder for the first 3.0 s ?

• 54 rad

• 42 rad

• 36 rad

• 28 rad

• 16 rad

A cylinder, with a moment of inertia ( I = 10 kgm² ), is rotating about a frictionless, fixed pivot with an angular velocity ω = 4t² + 2 . What is the net torque applied on the cylinder at t = 4.0 s ?

• 320 Nm

• 240 Nm

• 180 Nm

• 96 Nm

• 84 Nm

Two wheels are fixed to each other and are free to rotate about a frictionless axis through their concentric center. As shown in the diagram, four forces are exerted tangent to the wheels. The magnitude of the net torque is:

• zero

• FR

• 2 FR

• 4 FR

• 8 FR

A tire of mass M and radius R rolls on a flat track without slipping. If the angular velocity of the wheel is ω , what is its linear momentum?

• MωR

• Mω²R

• MωR²

• Mω²R²/2

• Zero

A toy car drives around a circular track with a radius of 10 m. When the car's velocity is instantaneously directed south, its acceleration is directed west at 10 m/s². When viewed from above, the car moves

• clockwise at 1 rad/s

• clockwise at 10 rad/s

• counterclockwise at 1 rad/s

• counterclockwise at 10 rad/s

• with constant velocity

Two masses, one with mass m and the other with mass 2m, are attached to a light rigid rod as shown above. When the system is released from rest, the rod begins to rotate with an angular acceleration magnitude of:

A rubber band ball of mass M, radius R, and I = (2/5) MR², rolls without slipping up an incline with an initial speed v. The ball reaches a maximum vertical height of:

A dart of mass m moves with a constant speed v₀ along the dashed line. The dart strikes a uniform disk of radius R. What is the magnitude of the angular momentum of the dart with respect to the center of the disk?

• zero

• mv₀R

• mv₀Rsinθ

• mv₀Rcosθ

• mv₀

A satellite of mass m moves with a constant speed v in a circular orbit of radius r. Which of the following statements are true?

I. Its angular speed is v/r.

II. Its tangential acceleration is zero.

III. The magnitude of its centripetal acceleration is constant.

• I only

• II only

• I and III only

• II and III only

• I, II, and III