Problem 9.23 A uniform-density 8 kg disk of radius 0.21 m is mounted on a nearly frictionless axle. Initially it is not spinning. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 36 N through a distance of 0.9 m. Now what is the angular speed?

4.63rad/s

Explanation:

The centripetal force is expressed as;

F = mv²/r

M is the mass of the disk = 8kg

v is the linear speed = wr

r is the radius = 0.21m

Force = 36N

Write the force in term of the angular velocity

F = m(wr)²/r

F = mw²r²/r

F = mw²r

36 = 8w²(0.21)

36 = 1.68w²

w² = 36/1.68

w² = 21.43

w = √21.43

w = 4.63rad/s

Hence the angular speed is now 4.63rad/s

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