Free Printable AP Physics C Rotation Questions

1.

A solid sphere with a density rho and radius R can be broken up into many small discs of thickness dz as shown, each with a moment of inertia equal to:

dI=\frac{1}{2}y^2dm

Which can be used to find the moment of inertia of the solid sphere?

a)

$\int_{-R}^R\ \frac{1}{2}\rho\left(R^2-z^2\right)\pi dz$

b)

$\int_{-R}^R\ \frac{1}{2}\rho\left(R^2-y^2\right)^2\pi dy$

c)

$\int_0^R\ \frac{1}{2}\rho\left(R^2-y^2\right)^2\pi dy$

d)

$\int_0^R\ \frac{1}{2}\rho\left(R^2-z^2\right)^2\pi dz$

2.

The uniform thin rod shown above has mass and length . What is the moment of the rod about an axis perpendicular to the rod and passing through point , which is halfway between the center and the end of the rod?
For a rod about its center:

I=\frac{1}{12}mL^2

a)

$\frac{1}{3}ml^2$

b)

$\frac{1}{48}ml^2$

c)

$\frac{7}{48}ml^2$

d)

$\frac{1}{6}ml^2$

3.

A woman sits on a spinning piano stool with her arms folded. When she extends her arms, which of the following occurs?

a)

She increases her moment of inertia, thereby increasing her angular speed.

b)

She increases her moment of inertia, thereby decreasing her angular speed.

c)

She decreases her moment of inertia, thereby increasing her angular speed.

d)

She decreases her moment of inertia, thereby decreasing her angular speed.

4.

A ball, rolling without slipping on a horizontal surface, encounters a frictionless, downward sloping ramp, as shown above. Which of the following correctly describes the motion of the ball on the ramp?

a)

Increasing translational speed with constant nonzero angular speed

b)

Increasing translational speed with decreasing angular speed

c)

Increasing translational speed with increasing angular speed

d)

Increasing translational speed with no angular speed

5.

Two identical cylindrical discs have a common axis. Initially one of the discs is spinning. When the two discs are brought into contact, they stick together. Which of the following is true?

a)

The total kinetic energy and the total angular momentum are unchanged from their initial values.

b)

Both the total kinetic energy and the total angular momentum are reduced by half.

c)

The total angular momentum is unchanged, but the total kinetic energy is reduced by half

d)

The total angular momentum is reduced by half, but the total kinetic energy is unchanged.

6.

A solid disk of mass M, radius R and rotational inertia I

is free to rotate about a fixed frictionless axis through its center. A force of constant direction and constant magnitude F is exerted on the disk.If the disk accelerates from rest at time t=0, through what angle θ does the disk rotate from t=0 to t=T?

a)

$\frac{FRT^2}{2M}$

b)

$\frac{FRT^2}{2I}$

c)

$\frac{FRT}{I}$

d)

$\frac{FT^2}{2I}$

7.

A disk initially at rest is acted upon by a constant net torque of τ. The disk spins for a period of t seconds and rotates an angular distance of Δθ. The same disk is brought to rest. The disk is now acted upon by a constant net torque of 2τ. The disk spins for the same period of t seconds. What is the new angular distance the disk rotates?

a)

$\frac{\Delta\theta}{2}$

b)

$2\Delta\theta$

c)

$\sqrt{2}\Delta\theta$

d)

$4\Delta\theta$

8.

In each case shown below, a 1.0 kg object is released from rest on a ramp of height 2 m from the bottom. Both spheres roll without slipping, and the blocks slide without friction. The ramps are identical in case A and C. The ramps in cases B and D are identical, but not as steep. Rank the speed of the objects when they reach the horizontal surface at the bottom of the ramp.

a)

B = C > A > D

b)

D> A > B = C

c)

C > B > A > D

d)

B = C > D > A

9.

A turntable with rotational inertia I is spinning on a frictionless axis at an initial angular speed of ω. A funnel is positioned above the turntable and drops syrup in a circle onto the turntable at a radius of R. If the funnel drops the syrup at a rate of S kg/s, what is the speed of the turntable as a function of time?

a)

$\omega\left(t\right)=\left(\frac{I}{I+StR}\right)\omega$

b)

$\omega\left(t\right)=\left(\frac{I}{I+SR^2}\right)\omega$

c)

$\omega\left(t\right)=\left(\frac{I}{I+StR^2}\right)\omega$

d)

$\omega\left(t\right)=\left(\frac{2I}{I+Srt}\right)\omega$

10.

A disk is initially rotating counterclockwise aroudn a fixed axis with angular speed . At time t = 0, the two forces shown in the figure are exerted on the disk. If counterclockwise is positive, which of the following could show the angular velocity of the disk as a function of time?

a)

b)

c)

d)

11.

A projectile of mass 0.2 kg and an initial velocity of 50 m/s

collides with the end of a blade attached to a turbine. The rotational inertia of the turbine is 12.5 . If the final rebound velocity of the projectile after hitting a turbine blade is −25 m/s, which of the following is most nearly the rotational velocity of the turbine after the collision?

a)

3.2 rad/s

b)

5.5 rad/s

c)

10.0 rad/s

d)

15.0 rad/s

12.

A horizontally-mounted disk with moment of inertia I spins about a frictionless axle. At time t=0, the initial angular speed of the disk is ω. A constant torque τ is applied to the disk, causing it to come to a halt in time t. How much Power is required to dissipate the wheel’s energy during this time?

a)

$\frac{I\omega^2}{2t}$

b)

$\frac{I\omega}{t}$

c)

$\frac{I\omega^2}{2\tau}$

d)

$\frac{I\omega}{\tau}$

13.

A spool is made of two circular disks connected to the ends of a cylinder so that the centers are aligned. The cylinder is shown as the dashed circle, and the disk on one end of the cylinder is shown as the larger solid circle. The spool is at rest on a level surface. A string attached to the cylinder is pulled gently so that the spool can rotate without slipping on the surface at point P. A force F is pulled in the direction of arrow d, and the spool spins but does not roll across the table. If the string is pulled with a force of 2F, which of the directions indicated, if any, indicates a pull on the string that will cause the spool to spin but not roll across the table?

a)

a

b)

b

c)

c

d)

d

14.

A rigid bar with a mass M and length L is free to rotate about a frictionless hinge at a wall. The bar has a moment of inertia I = 1/3 ML2 about the hinge, and is released from rest when it is in a horizontal position as shown. What is the instantaneous angular acceleration when the bar has swung down so that it makes an angle of 30° to the vertical?

a)

$\frac{g}{3L}$

b)

$\frac{2g}{3L}$

c)

$\frac{3g}{4L}$

d)

$\frac{3g}{2L}$

AP Physics C Rotation Questions

Total questions: 14

Worksheet time: 16mins

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