Name: _______________________________
Angular Momentum – Practice
1. Find the location of the center of mass, the rotational inertia around the center of mass,
ICOM, and the inertia, I, around the rotational axis for each of the following. Assume the
connecting pieces have negligible mass.
Rotational Axis
A.
10 kg
2.0 m
2.0 m
30 kg
Rotational Axis
B.
40 kg
3.0 m
1.0 m
10 kg
2. Parallel Axis Theorem
A. What is the rotational inertia of a hoop rotated about its central axis?
R
M
B. If the rotational axis is moved to the edge of the hoop, what is the rotational
inertia?
M
3. The graph on the right gives angular speed versus
time for a thin rod that rotates around one end. The
scale on the  axis is set by s = 6.0 rad/s.
A. What is the magnitude of the rod's angular
acceleration?
B. At t = 4.0 s, the rod has a rotational kinetic
energy of 1.60 J. What is its kinetic energy
at t = 0?
4. A disk rotates about an axis at a radial distance h from the center of the disk. The
rotational inertia I of the disk about the axis as a function h is shown on the graph. The
scale on the I axis is set by IA = 0.050 kg · m2 and IB = 0.150 kg · m2. What is the mass of
the disk?
5. Trucks can be run on energy stored in a rotating flywheel, with an electric motor getting
the flywheel up to its top speed of 200π rad/s. One such flywheel is a solid, uniform
cylinder with a mass of 500 kg and a radius of 1.0 m.
A. What is the kinetic energy of the flywheel after charging?
B. If the truck uses an average power of 8.0 kW, for how many minutes can it operate
between chargings?
6. Two particles, each with mass m = 0.85 kg, are
fastened to each other, and to a rotation axis at O,
by two thin rods, each with length d = 5.6 cm and
mass M = 1.2 kg. The combination rotates around the
rotation axis with the angular speed  = 0.30 rad/s.
A. Measured about O, what is the total
rotational inertia of the setup?
B. Measured about O, what is the total kinetic energy?
7. A uniform solid block has a mass of 0.172 kg and edge lengths
of a = 3.5 cm, b = 8.4 cm, and c = 1.4 cm. Calculate its rotational
inertia about an axis through one corner and perpendicular to the
large faces.
8. Merry-Go-Round – Round I: A young girl originally at the center of the merry-go-round
walks to the edge. Find f in revolutions per second and radians per second.
o = 1.0 rev/5.0 s
mGirl = 40 kg
I = 500. kg m2
R = 2.0 m
R
I

9. Merry-Go-Round – Round II: The same young girl is running on a path tangential to the
rim of the merry-go-round hops onto the edge and remains there. Find f.
o = 0
mGirl = 40 kg
I = 500. kg m2
R = 2.0 m
vo = 2.5 m/s
R
vo
10. A cylinder having a mass of 2.0 kg can rotate about
its central axis through point O. Forces are applied as
shown: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, and F4 = 5.0
N. Also, r = 5.0 cm and R = 12 cm. Find the magnitude
and direction of the angular acceleration of the
cylinder. (During the rotation, the forces maintain
their same angles relative to the cylinder.)
I

11. Two lumps of clay, 1.0 kg each, are
connected by a massless rod and are initially
1.0 kg
at rest. A third lump of clay of mass 1.0 kg
strikes the bottom lump of clay at 3.0 m/s
and sticks.
A. Find the center of mass of the three
lumps just after the moving lumps
strikes bottom lump.
2.0 m
1.0 kg
3.0 m/s
B. Find the velocity of the center of mass just after the collision.
C. Find  of the system just after the collision.
D. Write KRotation in terms of I and L.
1.0 kg
Solutions:
1. A. xCM = 3.0 m from left
B. xCM = 0.80 m from left
2. A. MR2
B. 2MR2
3. A. 1.5 rad/s2
4. 2.5 kg
5. A. 4.9 x 107 J
ICM = 120 kg m2
Irot = 160 kg m2
ICM = 128 kg m2
Irot = 370 kg m2
B. 0.40 J
B. 1.0 x 102 min
6. A. 0.023 kg m2 B. 1.1 x 10-3 J
7. 4.7 x 10-4 kg m2
8. 0.15 rev/s
9. 0.30 rad/s
10. 9.7 rad/s2
11. A. 0.67 m from bottom
B. 1.0 m/s
C. 0.75 rad/s
D. L2/2I
2