Chapter 9 Drill
The answers and explanations can be found in Chapter 17.
5. Joe and Alice are sitting on opposite ends of a seesaw.
Section I: Multiple Choice The fulcrum is beneath the center of the seesaw, which
has a length of 4 m. Given that Joe’s mass is 60 kg and
Alice’s mass is 30 kg, what will be the magnitude of the
1. A compact disc has a radius of 6 cm. If the disc rotates net torque on the seesaw when it is perfectly level?
about its central axis at an angular speed of 5 rev/s, what
is the linear speed of a point on the rim of the disc? (A) 300 N•m
(B) 600 N•m
(A) 0.3 m/s (C) 900 N•m
(B) 1.9 m/s (D) 1,200 N•m
(C) 7.4 m/s (E) 1,500 N•m
(D) 52 m/s
(E) 83 m/s
suspension
2. A compact disc has a radius of 6 cm. If the disc rotates point
about its central axis at a constant angular speed of 5
rev/s, what is the total distance traveled by a point on the 60
rim of the disc in 40 min?
(A) 180 m
L
(B) 360 m
(C) 540 m
(D) 720 m
(E) 4.5 km
m
3. A disc starts at rest and experiences constant angular
acceleration of 4 rad/s2. When the disc has gone through
a total angular displacement of 50 rad, what is its
angular speed? 6. In the figure above, what is the torque about the pendu-
lum’s suspension point produced by the weight of the
(A) 12 rad/s bob, given that the length of the pendulum, L, is 80 cm
(B) 15 rad/s and m = 0.50 kg?
(C) 16 rad/s
(D) 20 rad/s (A) 0.5 N•m
(E) 23 rad/s (B) 1.0 N•m
(C) 1.7 N•m
(D) 2.0 N•m
4. An object, originally at rest, begins spinning under (E) 3.4 N•m
uniform angular acceleration. In 10 s, it completes an
angular displacement of 60 rad. What is the numerical
value of the angular acceleration?
(A) 0.3 rad/s2
(B) 0.6 rad/s2
(C) 1.2 rad/s2
(D) 2.4 rad/s2
(E) 3.6 rad/s2
Rotational Motion | 261
9. The moment of inertia of a solid uniform sphere of mass
2
M and radius R is given by the equation I = 5 MR 2. Such
a sphere is released from rest at the top of an inclined
plane of height h, length L, and incline angle θ. If the
m M sphere rolls without slipping, find its speed at the bottom
of the incline.
10
7. A uniform meter stick of mass 1 kg is hanging from a (A) 7
gh
thread attached at the stick’s midpoint. One block of 5
mass m = 3 kg hangs from the left end of the stick, and (B) 2
gh
another block, of unknown mass M, hangs below the 80 (C) 7
gh
2
cm mark on the meter stick. If the stick remains at rest
in the horizontal position shown above, what is M? (D) 2
7
gL sin θ
(A) 4 kg (E) 7
gL sin θ
10
(B) 5 kg
(C) 6 kg
(D) 8 kg 10. When a cylinder rolls down an inclined plane without
(E) 9 kg slipping, which force is responsible for providing the
torque that causes rotation?
8. What is the rotational inertia of the following body (A) The force of gravity parallel to the plane
about the indicated rotation axis? (The masses of the (B) The force of gravity perpendicular to the plane
connecting rods are negligible.) (C) The normal force
(D) The force of static friction
rotation (E) The force of kinetic friction
axis
m m
8
3 L
m m
L L
(A) 4mL2
32
(B) 3 mL
2
64
(C) mL2
9
128 2
(D) mL
9
256
(E) mL2
9
262 | Cracking the AP Physics C Exam
Section II: Free Response
1. In the figure below, the pulley is a solid disk of mass M and radius R, with rotational inertia MR2/2. Two blocks, one of mass m1
and one of mass m2 , hang from either side of the pulley by a light cord. Initially the system is at rest, with Block 1 on the floor
and Block 2 held at height h above the floor. Block 2 is then released and allowed to fall. Give your answers in terms of m1 , m2 ,
M, R, h, and g.
M
R
Block 2
m2
h
Block 1
m1
(a) What is the speed of Block 2 just before it strikes the ground?
(b) What is the angular speed of the pulley at this moment?
(c) What’s the angular displacement of the pulley?
(d) How long does it take for Block 2 to fall to the floor?
Rotational Motion | 263
2. The diagram below shows a solid uniform cylinder of radius R and mass M rolling (without slipping) down an inclined plane of
incline angle θ. A thread wraps around the cylinder as it rolls down the plane and pulls upward on a block of mass m. Ignore the
rotational inertia of the pulley.
(a) Show that “rolling without slipping” means that the speed of the cylinder’s center of mass, vcm , is equal to Rω, where ω is
its angular speed.
(b) Show that, relative to P (the point of contact of the cylinder with the ramp), the speed of the top of the cylinder is 2vcm.
vc 2v
m cm
P
(c) What is the relationship between the magnitude of the acceleration of the block and the linear acceleration of the
cylinder?
(d) What is the acceleration of the cylinder?
(e) What is the acceleration of the block?
264 | Cracking the AP Physics C Exam
3. Two slender uniform bars, each of mass M and length 2L, meet at right angles at their midpoints to form a rigid assembly that’s
able to rotate freely about an axis through the intersection point, perpendicular to the page. Attached to each end of each rod is a
solid ball of clay of mass m. A bullet of mass mb is shot with velocity v as shown in the figure (which is a view from above of the
assembly) and becomes embedded in the targeted clay ball.
bullet
mb
v
θ
m
M
m
m
M
L L
(a) Show that the moment of inertia of each slender rod about the given rotation axis, not including the clay balls, is ML2/3.
(b) Determine the angular velocity of the assembly after the bullet has become lodged in the targeted clay ball.
(c) What is the resulting linear speed of each clay ball?
(d) Determine the ratio of the final kinetic energy of the assembly to the kinetic energy of the bullet before impact.
Rotational Motion | 265
