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

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?

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?