A 55.0-kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.800 m around the pole. Determine the force exerted by the horizontal rope on her arms.

You drop two balls from a tower, one of mass m and the other of mass 2m. Just before they hit the ground, which ball, if either, has the larger kinetic energy? Explain.

In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates in a horizontal circle. A trainee riding in the chamber of a centrifuge rotating with a constant angular speed of 2.5 rad/s experiences a centripetal acceleration of 3.2 times the acceleration due to gravity. In a second training exercise, the centrifuge speeds up from rest with a constant angular acceleration. When the centrifuge reaches an angular speed of 2.5 rad/s, the trainee experiences a total acceleration equal to 4.8 times the acceleration due to gravity. (a) How long is the arm of the centrifuge? (b) What is the angular acceleration of the centrifuge in the second training exercise?

A dentist’s drill starts from rest. After $3.20\mathrm{~ s}$ of constant angular acceleration, it turns at a rate of $2.51 \times 10^4\mathrm{ ~rev/min}$. Determine the angle (in radians) through which the drill rotates during this period.

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.60 m and 1.02 m, respectively. The respective rotational speeds are 450 rev/min and 4 138 rev/min. Calculate the speeds of the tips of both rotors. Compare these speeds with the speed of sound, 343 m/s.

Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g ($88 .2 m/s^2$) without losing consciousness. (a) If a human centrifuge has a radius of 4.50 m, what angular speed results in a centripetal acceleration of 9g? (b) What linear speed would a person in the centrifuge have at this acceleration?

An adventurous archeologist (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.0 m long, and his speed at the bottom of the swing is 8.00 m/s. The archeologist doesn’t know that the vine has a breaking strength of 1 000 N. Does he make it across the river without falling in?

What is the tangential acceleration of a bug on the rim of a 10.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 78.0 rev/min in 3.00 s?

A wheel has a radius of 4.1 m. How far (path length) does a point on the circumference travel if the wheel is rotated through angles of (a) $30 ^ { \circ }$, (b) 30 rad, and (c) 30 rev, respectively?

A potter’s wheel moves uniformly from rest to an angular speed of 1.00 rev/s in 30.0 s. Find its angular acceleration in radians per second per second.

What is a magnetic material able to do?

It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

The International Space Station has a mass of $4.19 \times 10^{5}$ kg and orbit s at a radius of $6.79 \times 10^{6}$ m from the center of Earth. Find the space station's gravitational potential energy.

A 40.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 18.0 m. What force does the seat exert on the child when the child is halfway between the top and bottom?