The angular position of a particle moving in a circular path is θ = (5t⁴ /40)-(t³ /3), where θ is in radians and t is in seconds. What is its angular acceleration at t = 10 s?
Options

Question

The angular position of a particle moving in a circular path is θ = (5t⁴ /40)-(t³ /3), where θ is in radians and t is in seconds. What is its angular acceleration at t = 10 s?

G1 Physics · Accepted Answer

Given, θ = 5t⁴ ÷ 40 - t³ ÷ 3 = t⁴ ÷ 8 - t³ ÷ 3. Angular velocity is ω = dθ ÷ dt = t³ ÷ 2 - t². Angular acceleration is α = dω ÷ dt = 3t² ÷ 2 - 2t. At t = 10 s, α = 3(10)² ÷ 2 - 2(10) = 150-20 = 130 rad·s⁻². Correct option: C.