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Mastering Problems Chapter 8 section 1 Name ______________________ 1. A wheel is rotated so that a point on the edge moves through 1.50 m. The radius of the wheel is 2.50 m. Through what angle in radians is the wheel rotated? 2. The outer edge of a truck tire that has a radius of 45 cm has a velocity of 23 m/s. What is the angular velocity of the tire in rad/s? 3. A steering wheel is rotated through 128⁰. Its radius is 22 cm. How far would a point on the steering wheel’s edge move.? 4. A propeller spins at 1880 rev/ min. a. What is its angular velocity in rad/s? b. What is the angular displacement of the propeller in 2.50 s? 5. The propeller in the previous problem slows from 475 rev/ min in 4.00 seconds. What is its angular acceleration? 6. A wheel with a radius of 9.00 m rotates at 2.50 rad/s. How fast does a point 7.00 cm from the center travel? 7. A washing machine’s two spin cycles are 328 rev/ min and 542 rev/min. The diameter of the drum is 0.43 m. a. What is the ratio of the centripetal accelerations for the fast and slow spin cycles? Recall that ac = v2/ r and v = rω. b. What is the ratio of the linear velocity of an object at the surface of the drum for the fast and slow spin cycles? 8. Find the maximum centripetal acceleration in terms of g for the washing machines in problem 7. 9. A laboratory ultracentrifuge is designed to produce a centripetal acceleration of 0.35 x 106 g at a distance of 2.50 m from the axis. What angular velocity in rev/min is required? 10. Jupiter, the largest planet in our solar system, rotates around its own axis in 9.84 h. The diameter of Jupiter is 1.43 x 108m. a. What is the angular speed of Jupiter’s rotation in rad/s? b. What is linear speed of a point on Jupiter’s equator due to Jupiter’s rotation? 11. A computer disk drive optimizes the data transfer rate by rotating the disk at a constant angular speed of 34.1 rad/s while it is being read. When the computer is searching for one of your files, the disk spins for 0.892s. a. What is the angular displacement of the disk during this time? b. Through how many revolutions does the disk turn during this time? 12. You are doing your laundry. When the washing machine goes into its spin cycle the tub starts from an angular speed of 2.30 rad/s, then speeds up smoothly for 8.00 s, until it is turning 5.00 rev/s. Calculate the angular acceleration of the tub during this time. 13. One of the beaters of an electric mixer has a diameter of 4.60 cm. What is the centripetal acceleration of the outer part of a blade as it rotates at a rate of 1200 rev/min? 13. A tractor wheel has a radius of 0.84 m. How far does a point on the wheel’s edge move when the wheel is rotated through an angle of 67⁰?