A particle moves on a circle such that θ = t². At t = 2 s, the ratio $a_c/aₜ$ is:
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A particle moves on a circle such that θ = t². At t = 2 s, the ratio a_c/aₜ is:

G1 Physics · Accepted Answer

ω=dθ/dt=2t, so at t=2 s, ω=4 rad/s. α=dω/dt=2 rad/s². Therefore a_c/aₜ = (Rω²)/(Rα) = ω²/α = 16/2 = 8.