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Asked in NEET 1992 · Change of kinetic energy and momentum
Given: uniform circular motion of speed v; compare two diametrically opposite points.
Idea: speed decides the kinetic energy, but momentum is a vector and carries the direction too.
At the first point take ⃗p₁=Mv along the tangent; half a turn later the tangent has reversed, so ⃗p₂=-Mv.
Δ⃗p=⃗p₂-⃗p₁=-Mv-Mv, of magnitude 2Mv.
The kinetic energy is 1/2Mv² at both points, so it does not change.
Momentum changes by 2Mv.
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