A particle describes an angle θ in a circular path with a constant speed ν. Find the (a) change in the velocity of the particle and (b) average acceleration of the particle during the motion in the curve (circle).
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Solution
a. As the particle moves from P to Q, the velocity turns through an angle Θ. Then, |Δ→v|=√v21+v22−2v1v2cosΘ
=√v2+v2−2vvcosΘ = 2vsinΘ2
b. The time of motion is Δt=RΘ/v.Then, average acceleration is |→aav|=→vΔt. Substituting |Δ→v and |Δv, we have |→aav|=2vsinΘ2RΘv=2v2RΘsinΘ2