A particle moves on a circle with angular speed ω = t² + 2t. At t = 2 s, the ratio aₜ/ $a_c$ is:
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A particle moves on a circle with angular speed ω = t² + 2t. At t = 2 s, the ratio aₜ/a_c is:

G1 Physics · Accepted Answer

At t=2 s, ω=2²+2(2)=8 rad/s. Angular acceleration α=dω/dt=2t+2=6 rad/s². Therefore aₜ/a_c = (Rα)/(Rω²)=α/ω²=6/64=3/32.