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Angular velocity or acceleration from a given theta(t) or alpha(t)

This type of question, asked 3 times: 28 Jun 2022, 23 Jan 2025, 2 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    28 Jun 2022

    92
    A ball is spun with angular acceleration α=6t2−2t\alpha = 6t^{2}- 2t where tt is in second and α\alpha is in rads−2rads^{- 2}. At t=0t = 0, the ball has angular velocity of 10 rads−1rads^{- 1} and angular position of 4rad4rad. The most appropriate expression for the angular position of the ball is:

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  2. Question 2

    23 Jan 2025

    82
    A circular disk of radius RR meter and mass M kgM\text{ }kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ(t)=5t2−8t\theta(t) = 5t^{2}- 8t, where θ(t)\theta(t) is the angular position of the rotating disc as a function of time tt. How much power is delivered by the applied torque, when t=2 st = 2\text{ }s ?

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  3. Question 3

    2 Apr 2026 S1

    6
    A particle is rotating in a circular path and at any instant its motion can be described as θ=5t440−t33\theta=\frac{5t^{4}}{40}-\frac{t^{3}}{3}. The angular acceleration of the particle after 10 seconds is ____\_\_\_\_ rad/s2rad/s^{2}.

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