Q126 / 180 · COMEDK 2026 (9 May Shift 1) · Physics
A particle starts rotating from rest. The instantaneous angular displacement is $\theta = 3t^3 - t^2$, where $\theta$ is in radian and t in s; The angular velocity at $t = 1$ s is
- A$9\ rads^{-1}$
- B$3\ rads^{-1}$
- Correct answerC$7\ rads^{-1}$
- D$1\ rads^{-1}$
Solution
The angular displacement is given by $\theta = 3t^3 - t^2$.
The angular velocity $\omega$ is the rate of change of angular displacement with respect to time, given by $\omega = \dfrac{d\theta}{dt}$.
Differentiating $\theta$ with respect to $t$:
$\omega = \dfrac{d}{dt}(3t^3 - t^2) = 9t^2 - 2t$
Substituting $t = 1$ s:
$\omega = 9(1)^2 - 2(1) = 7 \text{ rad s}^{-1}$
Answer: $7\ rads^{-1}$
The angular velocity $\omega$ is the rate of change of angular displacement with respect to time, given by $\omega = \dfrac{d\theta}{dt}$.
Differentiating $\theta$ with respect to $t$:
$\omega = \dfrac{d}{dt}(3t^3 - t^2) = 9t^2 - 2t$
Substituting $t = 1$ s:
$\omega = 9(1)^2 - 2(1) = 7 \text{ rad s}^{-1}$
Answer: $7\ rads^{-1}$
Hence, the correct answer is option: 'C'.