A particle travels at a uniform linear speed around a circle of radius r = 0.5 m, completing one revolution in 12 s. a. What is the value of the linear speed v? b. Find the particles angular speed. c. What are the angle and arc length s swept out by the particle in 4 s?

It takes 2 radians (rad) to get around a circle, which Is the same as 360 . How many radians are in 1 ?

A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity assuming a constant speed?

A disk 8.00 cm in radius rotates at a constant rate of 1200 rev/min about its central axis. Determine (a) its angular speed in radians per second, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on the rim, and (d) the total distance a point on the rim moves in 2.00 s.

At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

A digital audio compact disc carries data, each bit of which occupies 0.6 m along a continuous spiral track from the inner circumference of the disc to the outside edge. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.30 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.30 cm, and (b) at the end of the recording, where the spiral has a radius of 5.80 cm. (c) A full-length recording lasts for 74 min 33 s. Find the average angular acceleration of the disc. (d) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays. (e) Find the total length of the track.

Keratinocytes are the most common cells in the skins outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body diameter of 1.00 105 m (10 m), what minimum angular speed would be required to produce the observed linear speed of 1.67 107 m/s (10 m/min)? (b) How many complete revolutions would be required for the cell to roll a distance of 5.00 103 m? (Because of slipping as the cells roll, averages of observed angular speeds and the number of complete revolutions are about three times these minimum values.)

What is (a) the angular speed and (b) the linear speed of a point on Earth’s surface at latitude 30N . Take the radius of the Earth to be 6309 km. (c) At what latitude would your linear speed be 10 m/s?

A flea is at point on a horizontal turntable, 10.0 cm from the center. The turntable is rotating at 33.3 rev/min in the clockwise direction. The flea jumps straight up to a height of 5.00 cm. At takeoff, it gives itself no horizontal velocity relative to the turntable. The Ilea lands on the turntable at point . Choose the origin of coor-dinates to be at the center of the turntable and the positive xaxis passing through at the moment of takeoff. Then the original position of the flea is 10.0i cm. (a) Kind die position of point when die Ilea lands. (b) Find die position of point when the flea lands.