A particle moves on a circle with angular speed ω = ktⁿ, where k>0, n>0 and t>0. Let φ be the angle made by the net acceleration with the inward radial direction. Which statements are correct?
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Question

A particle moves on a circle with angular speed ω = ktⁿ, where k>0, n>0 and t>0. Let φ be the angle made by the net acceleration with the inward radial direction. Which statements are correct?

G1 Physics · Accepted Answer

Angular acceleration α=dω/dt=nktⁿ⁻¹. Since tanφ=aₜ/a_c=(Rα)/(Rω²)=α/ω², we get tanφ = nktⁿ⁻¹/(k²t²ⁿ) = n/(ktⁿ⁺¹). For positive n and k this decreases with time, so φ decreases. Radius cancels, so it does not affect φ.