4.20 kg and it exerts a force tangent to the
edge of the pulley. What is the angular
acceleration of the pulley?
rad/s^22.2 A string is wound tight around the spindle of a top, and then pulled to spin the top. While it is pulled, the string exerts a
constant torque of 0.150 N·m on the top. In the first 0.220 s of its motion, the top reaches an angular velocity of 12.0 rad/s.
What is the moment of inertia of the top?
kg·m^2
2.3 A wheel with a radius of 0.71 m is mounted
horizontally on a frictionless vertical axis. A toy
rocket is attached to the edge of the wheel, so
that it makes a 72° angle with a radius line, as
shown. The moment of inertia of the wheel
and rocket is 0.14 kg·m^2. If the rocket starts
from rest and fires for 8.4 seconds with a
constant force of 1.3 N, what is the angular
velocity of the wheel when the rocket stops
firing?
rad/sSection 3 - Calculating the moment of inertia
3.1 Four small balls are arranged at the corners of a rigid metal square with sides of length 3.0 m. An axis of rotation in the plane
of the square passes through the center of the square, and is parallel to two sides of the square. On one side of the axis, the
two balls have masses 1.8 kg and 2.3 kg; on the other side, 1.5 kg and 2.7 kg. The mass of the square is negligible compared
to the mass of the balls. What is the moment of inertia of the system for this axis?
kg·m^2
3.2 For the same arrangement as in the previous problem, what is the moment of inertia of the system of balls for the axis that
is perpendicular to the plane of the square, and passes through its center point?
kg·m^2
3.3 Four balls are connected by a straight rod. One end of the rod is painted blue. The first ball has mass 1.0 kg and is 1.0 m
from the blue end of the rod, the second ball has mass 2.0 kg and is 2.0 m from the blue end, and so on for the other two
balls. The mass of the rod is negligible compared to the mass of the balls. What is the moment of inertia of this system for an
axis of rotation perpendicular to the rod and touching the blue end?
kg·m^2
3.4 Four small balls of identical mass 2.36 kg are
arranged in a rigid structure as a regular
tetrahedron. (A regular tetrahedron has four
faces, each of which is an equilateral triangle.)
Each edge of the tetrahedron has length
3.20 m. What is the moment of inertia of the
system, for an axis of rotation passing
perpendicularly through the center of one of
the faces of the tetrahedron?
kg·m^2Section 4 - A table of moments of inertia
4.1 A tire of mass 1.3 kg and radius 0.34 m experiences a constant net torque of 2.1 N·m. Treat the tire as though all of its mass
is concentrated at its rim. How long does it take for the tire to reach an angular speed of 18 rad/s from a standing stop?
s
4.2 A hollow glass holiday ornament in the shape of a sphere is suspended on a string that forms an axis of rotation through the(^202) Copyright 2007 Kinetic Books Co. Chapter 10 Problems