An athlete whirls a discuss in a circle of radius 80.0 cm. At a certain instant, the athlete is rotating at 10 rad/s and the angular speed is increasing at 50.0 rad/s². For this instant, find the tangential and centripetal components of the acceleration of the discuss and the magnitude of the acceleration. (89.4 m/s²)

What is the average speed in mi/h of a person at the equator as a result of the Earths rotation? (Take the radius of the Earth to be RE = 4000 mi.)

A runner taking part in the 200-m dash must run around the end of a track that has a circular arc with a radius of curvature of 30.0 m. The runner starts the race at a constant speed. If she completes the 200-m dash in 23.2s and rum at constant speed throughout the race, what is her centripetal acceleration as she runs the curved portion of the track?

Suppose the polar ice sheets broke free and floated toward Earth’s equator without melting. What would happen to Earth’s angular velocity?

Olympic ice skaters are able to spin at about 5 rev/s. (a) What is their angular velocity in radians per second? (b) What is the centripetal acceleration of the skater's nose if it is 0.120 m from the axis of rotation? (c) An exceptional skater named Dick Button was able to spin much faster in the 1950s than anyone since—at about 9 rev/s. What was the centripetal acceleration of the tip of his nose, assuming it is at 0.120 m radius? (d) Comment on the magnitudes of the accelerations found. It is reputed that Button ruptured small blood vessels during his spins.

(a) What is the angular speed of the second hand of a clock? (b) What is the direction of as you view a clock hanging on a vertical wall? (c) What is the magnitude of the angular acceleration vector of the second hand?

Can tangential acceleration change the speed of a particle undergoing circular motion?

A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is 13.5kgm2 and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is 3.4kgm2 and she has 2.0 s to do the flips in the air?

In circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction. Explain your answer.

A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.