Question

A wheel of radius R is rolling without slipping along a flat surface. The center of...

A wheel of radius R is rolling without slipping along a flat surface. The center of the wheel is moving with the constant horizontal velocity v.

a) Show that for the wheel not to slip, the angular velocity of the wheel must be ω = v/R.

b) What is the velocity of a point on the wheel that is in contact with the ground (Measured in a coordinate system on the ground).

c) What is the velocity of a point on top of the wheel?

d) What is the acceleration of the point on the wheel that is in contact with the ground (relative to the ground).

c) What is the acceleration of the point on the top of the wheel?

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Answer #1

as the body is rolling = translating +rotating Hence it will be sum of two velocities.

For acceleration are the centre of the wheel is moving with constant speed sp Translational acceleration will be zero only rotational acceleration will contribute which is same for all points on the wheel.

(E) part has also the same acceleration = (angular frequency) × (radius)^2

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