A solid uniform-density sphere is tied to a rope and moves (without spinning) in

Question

A solid uniform-density sphere is tied to a rope and moves (without spinning) in a cirdle with speed 10 m/s. The distance from the center of the circle to the center of the sphere is 1.9 m, the mass of the sphere is 8 kg, and the radius of the sphere is 0.72 m. (a) What is the angular speed ? angular speed- (b) What is the rotational kinetic energy of the sphere? Krot (c) What is the total kinetic energy of the sphere? Ktotal = radians/s question Details M14 9.2.023 [3220118 A uniform-density 9 kg disk of radius 0.40 m is mounted on a nearly frictionless axle. Initialy it is not spinning. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 39 N through a dstance of 0.8 m. Now what is the angular speed? radians/s Question Details MI4 9.3.027. [3220540 You pull straight up on the string of a yo-yo with a force 0.18 N, and while your hand is maving up a distance 0.10 m, the yo-yo moves down a distance 0.25 m. The mass of the yo-yo is 0.048 kg, and it was initially moving downward with speed 2.9 m's. (a) What is the increase in the translational kinetic energy of the yo-yo? Ktrans (b) What is the new speed of the yo-yo? (c) What is the increase in the rotational kinetic energy of the yo-yo? AKrot Question Details M14 9.3.028. [3220635 A string is wrapped around a disk of mass m 2.4 kg and radius R 0.09 m. Starting from rest, you pull the string with a constant force F 6 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x -0.11 m. your hand has moved a distance of d . 0.26 m. (a) At this instant, what is the speed of the center of mass of the disk? (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass?

Explanation / Answer

1)
a)
angular speed, w = v/r

= 10/1.9

= 5.26 rad/s

b) KE_rotational = (1/2)*I*w^2

= (1/2)*8*1.9^2*5.26^2

= 400 J

c) KE_total = 400 J

2)

Workdone = increase in kinetic energy

F*d = (1/2)*I*w^2

F*d = (1/2)*(m*R^2/2)*w^2

39*0.8 = (1/2)*(9*0.4^2/2)*w^2

==> w = 9.31 rad/s

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