A cylinder of mass $M$ and radius $R$ is resting on horizontal platform (which is prarllel to the x-y plane) with its axis fixed along the y-axis and free to rotate about its axis. The platform is given a motion in the x-direction given by $x = A c o s (ω t)$ . there is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder during its motion is ...........

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Solution

$F o r p u r e r o l l i n g a = α R, a n d a c c e l e r a t i o n o f t h e p l a t f o r m i s a = - A ω^{2} c o s ω t \Rightarrow α = \frac{- A ω^{2} c o s ω t}{R} \Rightarrow τ = \frac{1}{2} M R^{2} (\frac{- A ω^{2} c o s ω t}{R}) \Rightarrow τ_{m a x} = \frac{A ω^{2} M}{2}$

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Forpurerollinga=αR,andaccelerationoftheplatformisa=−Aω2cosωt⇒α=−Aω2cosωtR⇒τ=12MR2(−Aω2cosωtR)⇒τmax=Aω2M2

$F o r p u r e r o l l i n g a = α R, a n d a c c e l e r a t i o n o f t h e p l a t f o r m i s a = - A ω^{2} c o s ω t \Rightarrow α = \frac{- A ω^{2} c o s ω t}{R} \Rightarrow τ = \frac{1}{2} M R^{2} (\frac{- A ω^{2} c o s ω t}{R}) \Rightarrow τ_{m a x} = \frac{A ω^{2} M}{2}$