A particle of mass m moves along a circle of radius R. Find the modulus of the average vector of the force acting on the particle over the distance equal to a quarter of the circle, if the particle moves
(a) uniformly with velocity `v`,
(b) with constant tangential acceleration `w_tau`, the initial velocity being equal to zero.

Explanation

Let us sketch the diagram for the motion of the particle of mass m along the cirle of radius R and indicate x and y axis, as shown in figure.
(a) For the particle, change in momentum `Deltavecp=mv(-veci)-mv(vecj)`
so, `|Deltavecp|=sqrt2mv`
and time taken in describing quarter of the circle,
`Deltat=(piR)/(2v)`
Hence, `lt vecF ge(|Deltavecp|)/(Deltat)=(sqrt2mv)/(piR//2v)=(2sqrt2mv^2)/(piR)`
(b) In this case
`vecp_i=0` and `vecp_f=mw_it(-veci)`,
so `|Deltavecp|=mw_tt`
Hence, `|lt vecF gt|=(|Deltavecp|)/(t)=mw_t`