A particle is rotating in a circular path and at any instant its motion can be described as The angular acceleration

Question

A particle is rotating in a circular path and at any instant its motion can be described as $θ = \frac{5 t^{4}}{40} - \frac{t^{3}}{3} .$ The angular acceleration of the particle after 10 seconds is ________ $rad / s^{2}$ . [2026]

Smart Achievers · Accepted Answer

(3)

$θ = \frac{5 t^{4}}{40} - \frac{t^{3}}{3}$

$ω = \frac{d θ}{d t} = \frac{5}{40} (4 t^{3}) - \frac{3 t^{2}}{3} = \frac{t^{3}}{2} - t^{2}$

$α = \frac{d ω}{d t} = \frac{3 t^{2}}{2} - 2 t$

$at t = 10 s$

$α = \frac{3}{2} {(10)}^{2} - 2 \times 10 = 130 {rad/sec}^{2}$

Solution

Q.
A particle is rotating in a circular path and at any instant its motion can be described as $θ = \frac{5 t^{4}}{40} - \frac{t^{3}}{3} .$ The angular acceleration of the particle after 10 seconds is ________ $rad / s^{2}$ . [2026]

1 150

2 120

3 130

4 170

Ans.
(3)

$θ = \frac{5 t^{4}}{40} - \frac{t^{3}}{3}$

$ω = \frac{d θ}{d t} = \frac{5}{40} (4 t^{3}) - \frac{3 t^{2}}{3} = \frac{t^{3}}{2} - t^{2}$

$α = \frac{d ω}{d t} = \frac{3 t^{2}}{2} - 2 t$

$at t = 10 s$

$α = \frac{3}{2} {(10)}^{2} - 2 \times 10 = 130 {rad/sec}^{2}$

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