12. Rotational Kinematics

A car drives at a constant $15\mathrm{m}/\mathrm{s}$ along a curve on city street with a radius of $70\mathrm{m}$. What is the acceleration of the car?

The dwarf planet Ceres has a radius of $476\mathrm{km}$, a mass of $9.5\times {10}^{20}\mathrm{kg}$, and a free fall acceleration due to gravity of $0.28\mathrm{m}/{\mathrm{s}}^2$. What speed will a rock have if it is orbiting Ceres, right on the surface? Ceres has no atmosphere – so there are no issues with air resistance – but assume that there are no mountains or large boulders to impede the orbit.

A person runs ¼ of the way around a circular lake in 5.6 minutes. What is the person's angular speed?

FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particle's angular velocity at (b) t = 4s

Flywheels—rapidly rotating disks—are widely used in industry for storing energy. They are spun up slowly when extra energy is available, then decelerate quickly when needed to supply a boost of energy. A 20-cm-diameter rotor made of advanced materials can spin at 100,000 rpm.b. Suppose the rotor's angular velocity decreases by 40% over 30 s as it supplies energy. What is the magnitude of the rotor's angular acceleration? Assume that the angular acceleration is constant.

The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds.a. At what time does the motor reverse direction?

A 25 g steel ball is attached to the top of a 24-cm-diameter vertical wheel. Starting from rest, the wheel accelerates at 470 rad/s². The ball is released after ¾ of a revolution. How high does it go above the center of the wheel?

The angular velocity of a spinning gyroscope is measured every 0.5 s. The results and the best-fit line from a spreadsheet are shown in FIGURE P4.63.

a. What is the gyroscope's initial angular velocity, at t = 0 s?

FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshaft's angular acceleration at (b) t = 3s

A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad/s² for ½s, then coasts at a steady angular velocity for another ½s.b. Through how many revolutions has the disk turned?

Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble's speed and acceleration?

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. (b) How many revolutions does the merry-go-round make as it stops?

Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?