Systems of Particles and Rotational Motion
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Question : 11
Total: 33
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.
Solution:
Let M and R be mass and radius of the hollow cylinder and the solid sphere, then,
Moment of inertia of the hollow cylinder about its axis of symmetry,
I 1 = M R 2
Moment of inertia of the solid sphere about its axis through its centre
I 2 =
M R 2
Torqueτ = I α
whereα
I 1 α 1 = I 2 α 2
=
=
=
α 2 = 2.5 α 1 α 2 > α 1
fromω = ω 0 + α t , ω 0 t , ω 2 > ω 1 ,
Moment of inertia of the hollow cylinder about its axis of symmetry,
Moment of inertia of the solid sphere about its axis through its centre
Torque
where
from
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