(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A wheel of radius 20cm is pushed to move it on a rough horizontal surface. It is found to move through a distance of 60cm on the road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is

a)along the velocity of the wheel

b)opposite to the velocity of the wheel

c)perpendicular to the velocity of the wheel

d)zero

2. Relevant equations

3. The attempt at a solution

Let us suppose that the friction is static and thus pure rolling occurs. The friction will act in the forward direction ie along the direction of velocity.

Since pure rolling occurs

[itex]v=\omega r[/itex]

The angular displacement is 2∏ rad

The perimeter of the wheel is 2∏*0.2 metres

Since pure rolling occurs the linear distance covered should be equal to (2∏*0.2)metres as only one revolution occurs. But the actual linear distance covered is 0.6 m. This means that our assumption is incorrect and thus kinetic friction acts in the backward direction. So answer should be (b) but it is (a). Where is the fault?

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# Homework Help: Direction of frictional force

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