First slide

Dynamics of rotational motion about fixed axis

Question

Four objects with the same mass and radius are spinning freely about a diameter with the same angular speed. Arrange the work required to stop them in the decreasing order
a) Solid sphere b) Hollow sphere c) Disc d) Hoop

Moderate

A

d, b, c, a
B

a, b, c, d
C

b, a, d, c
D

c, a, b, d

Solution

Magnitude of work done, $W = K E_{f} - K E_{i}$
Since final KE is zero work done is equal to $K E_{i}$
Now $K E_{i} = \frac{1}{2} I ω^{2}$
$I_{s o l i d s p h e r e} = \frac{2}{5} M R^{2}, I_{h a l l o w s p h e r e} = \frac{2}{3} M R^{2}$
$I_{d i s c} = \frac{1}{2} M R^{2}, I_{h o o p} = M R^{2}$

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