A particle moves on a circular path of radius 4 m with speed 20 m/s. At an instant, its acceleration makes 37° with the inward radial direction. Find (i) the rate of increase of speed and (ii) the magnitude of acceleration.
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Question

A particle moves on a circular path of radius 4 m with speed 20 m/s. At an instant, its acceleration makes 37° with the inward radial direction. Find (i) the rate of increase of speed and (ii) the magnitude of acceleration.

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G1 Physics · Accepted Answer

Centripetal acceleration is v²/R=400/4=100 m/s². The total acceleration makes 37° with the radial direction, so tan37°=aₜ/a(c)= 3 4 \frac{3}{4} 4 3 ​ . Hence aₜ=75 m/s² and a=√(100²+75²)=125 m/s².