ow all steps in your solutions, beginning with the appropriate equations from th

Question

ow all steps in your solutions, beginning with the appropriate equations from the ations handout sheet. Include diagrams wherever appropriate. ? light string is wound around the rim of a 20.0cm radius solid cylinder with 6.00 k mass that is set on a frictionless axle at its center. The cylinder starts from rest, and begins to rotate in place when the string is pulled with constant 6.90 N force. a) Find the rotation rate of the cylinder in revolutions per minute when the kinetic energy of the cylinder reaches 22.8 joules. h) Find the angular acceleration of the cylinder. c) Find the length of string unwound from the cylinder when its kinetic energy reaches 22.8 J.

Explanation / Answer

a) KE = 1/2 I w^2

I = 1/2 M R^2

KE = 0.5*(0.5*6*0.2^2)*w^2 = 22.8

w=19.49 rad/s = 142.7 rpm

b)

torque = I alpha

torque = r F

6.9*.2 = 0.5*6*0.2^2*alpha

alpha = 11.5 rad/s^2

c) w^2 = w0^2 + 2 alpha theta

19.49^2 = 2*11.5*theta

theta = 19.49^2/(2*11.5)= 16.5 rad

L = r theta = 0.2*16.5= 3.3 m

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