Problem 1
A carnival swing is fixed on the end of an 8.0 -m-long beam. If the swing and
beam sweep through an angle of \(120^{\circ},\) what is the distance through
which the riders move?
Problem 2
A soccer ball of diameter \(31 \mathrm{cm}\) rolls without slipping at a linear
speed of \(2.8 \mathrm{m} / \mathrm{s} .\) Through how many revolutions has the
soccer ball turned as it moves a linear distance of \(18 \mathrm{m} ?\)
Problem 3
Find the average angular speed of the second hand of a clock.
Problem 4
Convert these to radian measure: (a) \(30.0^{\circ},\) (b) \(135^{\circ}\) (c)
\(\frac{1}{4}\) revolution, (d) 33.3 revolutions.
Problem 5
A bicycle is moving at \(9.0 \mathrm{m} / \mathrm{s} .\) What is the angular
speed of its tires if their radius is \(35 \mathrm{cm} ?\)
Problem 6
An elevator cable winds on a drum of radius \(90.0 \mathrm{cm}\) that is
connected to a motor. (a) If the elevator is moving down at $0.50 \mathrm{m} /
\mathrm{s},$ what is the angular speed of the drum? (b) If the elevator moves
down \(6.0 \mathrm{m},\) how many revolutions has the drum made?
Problem 7
Grace is playing with her dolls and decides to give them a ride on a merry-go-
round. She places one of them on an old record player turntable and sets the
angular speed at 33.3 rpm. (a) What is their angular speed in rad/s?
(b) If the doll is \(13 \mathrm{cm}\) from the center of the spinning turntable
platform, how fast (in \(\mathrm{m} / \mathrm{s}\) ) is the doll moving?
Problem 8
A wheel is rotating at a rate of 2.0 revolutions every \(3.0 \mathrm{s} .\)
Through what angle, in radians, does the wheel rotate in \(1.0 \mathrm{s} ?\)
Problem 10
Verify that all three expressions for radial acceleration $\left(v \omega,
v^{2} / r, \text { and } \omega^{2} r\right)$ have the correct dimensions for
an acceleration.
Problem 12
The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out. (a) What force keeps the people from falling out the bottom of the cylinder? (b) If the coefficient of friction is 0.40 and the cylinder has a radius of \(2.5 \mathrm{m},\) what is the minimum angular speed of the cylinder so that the people don't fall out? (Normally the operator runs it considerably faster as a safety measure.) (IMAGE CAN'T COPY)
