A particle moves in a circle of radius 1 m with initial angular speed 12 rad/s. From t=0 it has constant angular acceleration α, and after 2 s its speed becomes (480/π) rpm. It then continues with this attained speed. Determine: (i) α; (ii) tangential speed v(t); (iii) acceleration magnitudes at t=0.5 s and t=3 s; (iv) angular displacement at t=3 s.
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Question

A particle moves in a circle of radius 1 m with initial angular speed 12 rad/s. From t=0 it has constant angular acceleration α, and after 2 s its speed becomes (480/π) rpm. It then continues with this attained speed. Determine: (i) α; (ii) tangential speed v(t); (iii) acceleration magnitudes at t=0.5 s and t=3 s; (iv) angular displacement at t=3 s.

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G1 Physics · Accepted Answer

(480/π) rpm = (480/π)(2π/60)=16 rad/s. Thus α=(16-12)/2=2 rad/s². For r=1 m, v=ωr=12+2t up to 2 s and then 16 m/s. At 0.5 s, ω=13, so a=√[(ω²r)²+(αr)²]=√(169²+2²)=169.01 m/s²; at 3 s, a=16²=256 m/s². Angular displacement=12(2)+½(2)(2²)+16(1)=44 rad.