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Magazine 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 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 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 13
Objects that are at rest relative to Earth's surface are in circular motion due to Earth's rotation. What is the radial acceleration of an African baobab tree located at the equator?
Problem 17
A child swings a rock of mass \(m\) in a horizontal circle using a rope of
length \(L\). The rock moves at constant speed \(v\). (a) Ignoring gravity, find
the tension in the rope.
(b) Now include gravity (the weight of the rock is no longer negligible,
although the weight of the rope still is negligible). What is the tension in
the rope? Express the tension in terms of \(m, g, v, L,\) and the angle \(\theta\)
that the rope makes with the horizontal.
Problem 18
A conical pendulum consists of a bob (mass \(m\) ) attached to a string (length \(L\) ) swinging in a horizontal circle (Fig. 5.11 ). As the string moves, it sweeps out the area of a cone. The angle that the string makes with the vertical is \(\phi\) (a) What is the tension in the string? (b) What is the period of the pendulum?
Problem 19
A curve in a stretch of highway has radius \(R .\) The road is unbanked. The
coefficient of static friction between the tires and road is \(\mu_{s} .\) (a)
What is the fastest speed that a car can safely travel around the curve? (b)
Explain what happens when a car enters the curve at a speed greater than the
maximum safe speed. Illustrate with an FBD.
Problem 20
A highway curve has a radius of \(825 \mathrm{m}\). At what angle should the
road be banked so that a car traveling at $26.8 \mathrm{m} / \mathrm{s}(60
\mathrm{mph})\( has no tendency to skid sideways on the road? \)[$Hint: No
tendency to skid means the frictional force is zero. \(]\)
