Rotational MotionHard
Question
A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2 ) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :
Options
A.more than 3 but less than 6
B.more than 6 but less than 9
C.more than 9
D.less than 3
Solution
r × F = I × α
2(20t - 5t2) = 10α ⇒ α = 4t - t2
= 4t - t2
dϖ = (4t - t2) dt
ϖ = 2t 2 -
(on integration)
ϖ = 0 ⇒ t = 6 s
ϖ =
= 2t2 -
⇒
(on integration)
θ (in 6 s) = 36 rad
⇒ 2πn = 36
2(20t - 5t2) = 10α ⇒ α = 4t - t2
= 4t - t2 dϖ = (4t - t2) dt
ϖ = 2t 2 -
(on integration)ϖ = 0 ⇒ t = 6 s
ϖ =
= 2t2 - ⇒
(on integration)θ (in 6 s) = 36 rad
⇒ 2πn = 36
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