A solid uniform disk of mass M = 8.8 kg and radius R = 21 cm rests with its flat

Question

A solid uniform disk of mass M = 8.8 kg and radius R = 21 cm rests with its flat surface on a frictionless table (i.e., the axis of the cylinder is perpendicular to the table.) The diagram shows a top view. A string is wrapped around the rim of the disk and a constant force of F = 113 N is applied to the string. The string does not slip on the rim.

a) What is the acceleration of the center of mass?

a = ?? m/s2

b) What is the angular acceleration about the center of mass?

a = ?? rad/s2

The next 5 questions refer to a time 1.2 s after the force is first applied. c) How far has the disk moved?

d = ?? m

d) Through what angle has the disk turned?

q = ?? rad

e) What is the translational speed of the disk?

v = ?? m/s

f) What is the angular velocity about the center of the disk?

w = ?? rad/s

g) What is the total kinetic energy of the disk?

KE = ?? J

Explanation / Answer

I=0.5mr2=0.194 kgm2

a)a=F/m=113/8.8=12.84m/s2

b)=/I=Fr/I=122.32 rad/s2

c)d=0.5at2=9.245m

d)=0.5t2=88 radians

e)v=at=15.4m/s

f)=t=146.8 rad/s

g)KE=0.5mv2+0.5I2=3134J

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