# Rotation of plane

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A cylinder of mass M and radius R is resting on a horizontal platform (which is parallel 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 cos($\omega$t). There is no slipping between the cylinder and
platform. Find the maximum torque acting on the cylinder during its motion.

In the above question , I could not imagine what the question is asking .

There is no slipping between cylinder and plane at the point of contact. Therefore the linear acceleration $a=\ddot x$ of the plane is the same as the linear acceleration of the *circumference* of the cylinder (where contact is made). Angular and linear accelerations are related by $a=R\alpha$.
Hence we can differentiate to find the acceleration .  That is a = A$\omega$$^2cos\omegat . And a/R would be angular acceleration See my answer ## 1 Answer 3 votes Best answer we can differentiate to find the acceleration . That is a = Aω^2cosωt . And a/R would be angular acceleration . So maximum angular acceleration is A\omega$$^2$/R
Maximum torque = I$\alpha$ = (1/2)MRA$\omega$$^2$