1. A child is seated 1.2 meters from the center of a steadily rotating, circular merry-go-round which completes a single full rotation in 4.0 seconds. Based on this information calculate the child's (A) linear speed and (B) acceleration.
2. The platter of a computer hard disk rotates at 5400 revolutions per minute. Based on this information determine (A) the angular velocity of the disk, (B) the speed of the disk beneath the reading head situated 3.0 cm from the rotation axis, and (C) the linear acceleration at this point.
3. A single bit of computer data occupies 5 micrometers of length along the motion direction of its hard disk. Based on this information, calculate the number of bits per second the writing head the computer in Problem 2's hard disk can write when it is 3.0 centimeters from its rotational axis.
4. The rotor of a centrifuge is accelerated from rest to 2 x 10exp4 revolutions per minute in 5.0 minutes. Based on this information, calculate the average angular acceleration of the centrifuge.
5. Based on the information provided in problem 4 above, and assuming constant angular acceleration, calculate the total number of revolutions the centrifuge experienced during its acceleration period.
6. A bicycle slows down uniformly from v0 = 8.40 meters per second to rest over a distance of 115 meters. Each wheel and tire has an overall diameter of 68.0 cm. Based on this information calculate (A) the angular velocity of the wheels at the very start, (B) the total number of revolutions each wheel rotates in coming to rest, (C) the angular acceleration of the wheel, and (D) the time it took for the bicycle to come to a complete stop.
Answers:
1. (A) 1.9 m/s
(B) 3. m/sexp2
(B) 3. m/sexp22. (A) 570 rad/s (B)17 m/s(C) 9700 m/sexp2
(B)17 m/s(C) 9700 m/sexp23. 3.4 x 10exp6 bits per second
4. 7.0 rad/sexp2
5. 5.0x 10exp4 revolutions
6. (A) 24.7 rad/s (B) 53.8 revolutions
(B) 53.8 revolutions (C) -0.902 rad/sexp2 (D) 27.4 s
