Problem 1
The following angles are given in degrees. Convert them to radians: \(30^{\circ}, 45^{\circ}, 90^{\circ}, 180^{\circ}\).
Problem 2
The following angles are given in radians. Convert them to degrees: \(\pi / 6 \mathrm{rad}, 0.70 \mathrm{rad}, 1.5 \pi \mathrm{rad}, 5 \pi \mathrm{rad}\).
Problem 3
A CD rotates at \(22.0 \mathrm{rad} / \mathrm{s}\). What is its angular speed in revolutions per minute \((\mathrm{rpm})\) ?
Problem 4
A ceiling fan rotates at the rate of \(45^{\circ}\) every \(0.75 \mathrm{~s}\). What is the angular speed of the fan in radians per second?
Problem 5
An airplane propeller rotates with an angular speed of \(260 \mathrm{rad} / \mathrm{s}\). Through what angle does the propeller rotate in \(5.0 \mathrm{~s}\) ? Give your answer in both radians and degrees.
Problem 6
How much time does it take for a spinning baseball with an angular speed of \(38 \mathrm{rad} / \mathrm{s}\) to rotate through \(15^{\circ}\) ?
Problem 8
The hour hand on a certain clock is \(8.2 \mathrm{~cm}\) long. Find the tangential speed of the tip of this hand during normal operation.
Problem 9
The wheels of a car speed up from \(5.2 \mathrm{rad} / \mathrm{s}\) to \(7.9 \mathrm{rad} / \mathrm{s}\) in \(1.3 \mathrm{~s}\). What is the angular acceleration of the wheels?
Problem 10
As you start riding a bicycle, the wheels begin at rest and have an angular acceleration of \(2.3 \mathrm{rad} / \mathrm{s}^{2}\). What is the angular speed of the wheels after \(3.8 \mathrm{~s}\) ?
Problem 11
A bicycle wheel has rotated \(32^{\circ}\) counterclockwise from the reference line. Is this angular position positive or negative?
