Rotational and Translational Motion

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Prepared ByAnand

IIT Roorkie

Find the velocity vector at any point x distance away from the center of a Disc rolling in a horizontal plane and the case is

(a) Perfect Rolling (b) Vcm= 3w R Also trace the path followed by any

point x distance away and any point on the surface of disc

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A sphere rolls without slipping on a rough surface with center of mass has constant speed v0. If mass of the sphere is m and the radius is R, then find the angular momentum of the sphere about the point of contact.

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A plank of mass M rests on a smooth horizontal plane. A sphere of mass m is placed on the rough upper surface of the plank and the plank is given a velocity v in the direction of its length.Find the time after which the sphere begins pure rolling,if the coefficient of friction between the plank and the sphere is µ and the plank is sufficiently long.

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A light rod of length 1 m is constrained to move in a vertical plane. So that its ends are along x and y axis. Find the instantaneous axis of rotation of the rod when it makes an angle x with the horizontal

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A solid sphere is rolling on a rough horizontal surface with linear speed v collides elastically with a fixed, smooth vertical wall. Find the speed of sphere after it has started pure rolling in the backward direction.

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Problem of this lecture dayProblem of this lecture day

A rough and inelastic sphere of radius a rolling with a velocity v on a horizontal plane meets a fixed obstacle of height h. Show that if

a/(7a-5h) sqrt(10gh) <v< 7a/(7a-5h) sqrt (a-h)

The sphere will overcome the obstacle without bouncing

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a

H

V

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