A thin, light string is wrapped around the rim of a 3.65kg solid uniform disk th

Question

A thin, light string is wrapped around the rim of a 3.65kg solid uniform disk that is 33.0cm in diameter. A person pulls on the string with a constant force of 96.00N tangent to the disk, as shown in the figure below. The disk is not attached to anything and is free to move and turn.

Part A

Find the angular acceleration of the disk about its center of mass.

? = _____ rad/s2

Part B

Find the linear acceleration of its center of mass.

a = ______ m/s^2

Part C

If the disk is replaced by a hollow thin-walled cylinder of the same mass and diameter, what will be the angular acceleration of the disk about its center of mass?

? =_____ rad/s2

Part D

If the disk is replaced by a hollow thin-walled cylinder of the same mass and diameter, what will be the linear acceleration of its center of mass?

a =______ m/s2

? =_____ rad/s2

Part D

If the disk is replaced by a hollow thin-walled cylinder of the same mass and diameter, what will be the linear acceleration of its center of mass?

a =______ m/s2

Explanation / Answer

m = 3.65 kg, radius r = 0.165 m, F = 96 N
moment of inertia I = mr2/2
a) ? = F*r = I?
?? = Fr/I = 2F/(mr) = 318.8 rad/s2
b) F = ma,
?a = F/m = 26.3 m/s2
c) I' = mr2
? = Fr/I' = F/(mr) = 159.4 rad/s2
d) a = F/m = 26.3 m/s2

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