A string is wrapped around a uniform disk of mass M 19 kg a

A string is wrapped around a uniform disk of mass M = 1.9 kg and radius R = 0.08 m. (Recall that the moment of inertia of a uniform disk is (1/2)MR².) Attached to the disk are four low-mass rods of radius b = 0.16 m, each with a small mass m = 0.4 kg at the end. The device is initially at rest on a nearly frictionless surface. Then you pull the string with a constant force F = 32 N. At the instant when the center of the disk has moved a distance d = 0.031 m, a length w = 0.015 m of string has unwound off the disk.

(a) At this instant, what is the speed of the center of the apparatus?

v = ?????????? m/s

(b) At this instant, what is the angular speed of the apparatus?

1 = ???????????? radians/s

(c) You keep pulling with constant force 32 N for an additional 0.039 s. Now what is the angular speed of the apparatus?

2 = ?????????????? radians/s

Solution

a) At this instant, what is the speed of the center of the apparatus?

v = 10.8 m/s

(b) At this instant, what is the angular speed of the apparatus?

1 = 0.227 radians/s

(c) You keep pulling with constant force 32 N for an additional 0.039 s. Now what is the angular speed of the apparatus?

2 = 0.0031 radians/s