Consider a uniform disk of mass 1.5 kg and radius 0.10 m which is free to rotate

Question

Consider a uniform disk of mass 1.5 kg and radius 0.10 m which is free to
rotate about an axis perpendicular to the disk passing through its center. A force of
2.0 N is applied continuously to the disk at its edge tangent to the disk in the plane of
the disk.
a) What is the angular acceleration of the disk?
b) If the disk starts from rest, what is its angular momentum after it has turned
through an angle of 33 rad?
c) At the instant when it has turned through the 33-rad angle what is the linear
velocity of a point on the edge of the disk?

Explanation / Answer

MI of the disk = mr2/2

I = 1.5 x 0.12/2

I = 0.0075

now ,

a) I =

0.0075 x = 2 x 0.1

= 26.66 rad/s2

b) = 33rad

2 = 2

= (2 x 33 x 26.66)

= 41.94 rad/s

therefore, angular momentum = I = 0.0075 x 41.96 = 0.3147

c) v = r

v = 41.96 x 0.10

v = 4.196m/s

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