A cylinder of mass M, radius R is resting on a horizontal platform (which$$ is parallel to $$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 $$x-direction$$ given by $$x=acos$$⁡ωt There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is

Question

A cylinder of mass M, radius R is resting on a horizontal platform (which$$ is parallel to $$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 $$x-direction$$ given by $$x=acos$$⁡ωt There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is

Infinity Learn · Accepted Answer

The motion of platform is described by $$equationx=acos$$⁡ωt∴  velocity $$=dxdt=$$−aω$$sin$$⁡ωt and acceleration $$=d2xdt2=$$−aω$$2cos$$⁡ωtSO, $$amax=a$$ω$$2Now$$, τ$$max=I$$α$$max=IamaxR=12MR2a$$ω$$2R=12MRa$$ω$$2$$

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