Section 9 - Angular momentum of a rigid body
9.1 A thin rod 2.60 m long with mass 3.80 kg is rotated counterclockwise about an axis through its midpoint. It completes 3.70
revolutions every second. What is the magnitude of its angular momentum?
kg·m^2 /s
9.2 A 0.16 meter long, 0.15 kg thin rigid rod has a small 0.22 kg mass stuck on one of its ends and a small 0.080 kg mass stuck
on the other end. The rod rotates at 1.7 rad/s through its physical center without friction. What is the magnitude of the angular
momentum of the system taking the center of the rod as the origin? Treat the masses on the ends as point masses.
kg·m^2 /s
9.3 A solid cylinder is rotated counterclockwise around an axis at its base (one circular end). The axis lies in the plane of the
base, and passes through the center of the circle. The cylinder is 3.60 m long and has a radius of 0.870 m. Its mass is
2.30×10^4 kg and the center of the base opposite the axis has a tangential speed of 12.0 m/s. What is the cylinder's angular
momentum?
kg·m^2 /sSection 10 - Torque and angular momentum
10.1 An electric drill delivers a net torque of 15.0 N·m to a buffing wheel used to polish a car. The buffing wheel has a moment of
inertia of 2.30×10í^3 kg·m^2. At 0.0220 s after the drill is turned on, what is the angular velocity of the buffing wheel?
rad/s
10.2 A merry-go-round is 18.0 m in diameter and has a mass, unloaded, of 48,100 kg. It is fairly uniform in structure and can be
considered to be a solid cylindrical disk. The merry-go-round carries 28 passengers, who have an average mass of 68.5 kg
and all sit at a distance of 8.75 m from the center. The fully-loaded merry-go-round takes 48.0 s to reach an angular velocity
of 0.650 rad/s. (a) What is the moment of inertia of the loaded merry-go-round? (b) What constant net torque is applied to the
merry-go-round to reach this working speed?
(a) kg·m^2 (b) N·m
10.3 A string is wound around the edge of a solid 1.60 kg disk with a 0.130 m radius. The disk is initially at rest when the string is
pulled, applying a force of 6.50 N in the plane of the disk and tangent to its edge. If the force is applied for 1.90 seconds, what
is the magnitude of its final angular velocity?
rad/sSection 11 - Conservation of angular momentum
11.1 A 1.6 kg disk with radius 0.63 m is rotating freely at 55 rad/s around an axis perpendicular to its center. A second disk that is
not rotating is dropped onto the first disk so that their centers align, and they stick together. The mass of the second disk is
0.45 kg and its radius is 0.38 m. What is the angular velocity of the two disks combined?
rad/s
11.2 Two astronauts in deep space are connected by a 22 m rope, and rotate at an angular velocity of 0.48 rad/s around their
center of mass. The mass of each astronaut, including spacesuit, is 97 kg, and the rope has negligible mass. One astronaut
pulls on the rope, shortening it to 14 m. What is the resulting angular velocity of the astronauts?rad/s
11.3 A 27.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to
the edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk.
rad/s
11.4 A puck with mass 0.28 kg moves in a circle at
the end of a string on a frictionless table, with
radius 0.75 m. The string goes through a hole
in the table, and you hold the other end of the
string. The puck is rotating at an angular
velocity of 18 rad/s when you pull the string to
reduce the radius of the puck's travel to
0.55 m. Consider the puck to be a point mass.
What is the new angular velocity of the puck?
rad/s(^204) Copyright 2007 Kinetic Books Co. Chapter 10 Problems