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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 .

asked Dec 22, 2016 in Physics Problems by koolman (4,286 points)
Make a sketch. The cylinder (a circle in 2D) is fixed so that it can rotate about its axis (going into the page) but this axis does not change position. The plane (eg a horizontal line in 2D) in contact with the cylinder (eg tangent to the lowest point of the circle) moves horizontally, to and fro, causing the cylinder to turn and therefore causing angular acceleration. Torque is proportional to angular acceleration. So find the maximum angular acceleration then you can calculate the maximum torque.
Does the acceleration of plane is same as that of cylinder
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$$^2$cos$\omega$t . And a/R would be angular acceleration
See my answer

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we can differentiate to find the acceleration . That is a = Aω$^2$cosωt . 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$

answered Dec 23, 2016 by koolman (4,286 points)
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