Honors Physics
Rotational Motion & Equilibrium
Work sheet #6
Angular Momentum
Angular Momentum
1.
MC The units of angular momentum are (a) N  m, (b) kg  m s2 , (c) kg  m 2 s , (d) J  m. (c)
2.
MC The angular momentum may be increased by (a) decreasing the moment of inertia, (b)
decreasing the angular velocity, (c) increasing the product of the angular momentum and moment
of inertia, (d) none of these. (c)
3.
CQ A child stands on the edge of a rotating playground merry-go-round (the hand-driven type). He
then starts to walk toward the center of the merry-go-round. This results in a dangerous situation.
Why?
4.
 What is the angular momentum of a 2.0-g particle moving counterclockwise (as viewed from
above) with an angular speed of 5 rad s in a horizontal circle of radius 15 cm? (Give the
magnitude and direction.) 7.1104 kg  m 2 s toward you
5.
 A 10-kg rotating disk of radius 0.25 m has an angular momentum of 0.45 kg  m2 s. What is the
angular speed of the disk? 1.4 rad s
6.
 Compute the ratio of the magnitudes of the Earth’s orbital angular momentum and its rotational
angular momentum. Are these momenta in the same direction? Distance from earth to sun
1.5x1011m, radius of the earth is 6.4 x 106m Lorbital Lrotation  3.8  106 ; no
IE  Circular disks are used in automobile clutches and transmissions. When a rotating disk
couples to a stationary one through frictional force, the energy from the rotating disk can transfer to
the stationary one. (a) Is the angular speed of the coupled disks (1) greater than, (2) less than, or (3)
the same as the angular speed of the original rotating disk? Why? (b) If a disk rotating at 800 rpm
couples to a stationary disk with three times the moment of inertia, what is the angular speed of the
combination? Consider the angular momentum of the clutches. (a) (2) less than (b) 200 rpm
Answers
#3 Walking toward the center decreases the moment of inertia and so increases the rotational speed.
7.
#6 Orbital:
The Earth can be considered as a particle (great distance from the Earth to the Sun).
2 rad
o = (365)(24)(3600 s) = 1.99  107 rad/s, and Io = MR2.
So
Lo = Ioo = (6.0  1024 kg)(1.5  1011 m)2(1.99  107 rad/s) = 2.69  1040 kg·m2/s.
Spin: The Earth has to be considered as a sphere.
2
Is = 5 Mr2,
so
Therefore
Lo
2.69  1040
=
= 3.8  106 .
Ls
7.15  1033
2 rad
s = (24)(3600 s) = 7.27  105 rad/s, and
2
Ls = 5 (6.0  1024 kg)(6.4  106 m)2 (7.27  105 rad/s) = 7.15  1033 kg·m2/s.
No , these angular momenta are not in the same direction, because the Earth’s axis is tilted.
#7 IE  Circular disks are used in automobile clutches and transmissions. When a rotating disk
couples to a stationary one through frictional force, the energy from the rotating disk can transfer to
the stationary one. (a) Is the angular speed of the coupled disks (1) greater than, (2) less than, or (3)
the same as the angular speed of the original rotating disk? Why? (b) If a disk rotating at 800 rpm
couples to a stationary disk with three times the moment of inertia, what is the angular speed of the
combination? (a) (2) less than (b) 200 rpm