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Discussion Response Post to: ROLLING WITHOUT SLIPPING

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Soumen Goswami (2446)

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total posts: 1777
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Pure rolling can be studied as a combination of translational motion and rotational motion about CM.

In the translational part:
The velocity of each point of the wheel is same as the CM. So the lowermost point has a speed v rightwards.

In the rotational part,
Each point on the rim has a velocity

r directed along the tangent. So the lowermost point has a velocity

r directed leftward (Assuming clockwise rotation)

So the net velocity of the lowermost point is the sum of the forward velocity v and the backward velocity

r . If v =

r then the net velocity of the point of contact is v -

r = 0.

For the topmost point, the velocities due to translation and rotation are in the forward directions. So they add up to v +

r. If v =

r then topmost point moves with speed 2v.

All men dream but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity; but the dreamers of the day are dangerous men, for they may act their dream with open eyes to make it possible.

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