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Uniform angular retardation: rotations, angle or retardation before stopping

This type of question, asked 3 times: 19 Apr 2025 S1, 26 Apr 2025 S1, 11 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S1

    31
    When a ceiling fan is switched off, its angular velocity falls to (13)rd \left( \frac{1}{3} \right)^{\text{rd~}} while it makes 24 rotations. How many more rotations will it make before coming to rest?

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  2. Question 2

    26 Apr 2025 S1

    21
    A rigid body rotates about a fixed axis with variable angular velocity ( α−βt\alpha-\beta t ) at time tt, where α\alpha and β\beta are constants. The angle through which it rotates before it comes to rest is

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  3. Question 3

    11 Apr 2026 S1

    106
    A wheel is rotating at 600600 rpm about its axis of rotation. When the power is cut off, it comes to rest in half a minute. Its angular retardation expressed in rad/s2\mathrm{rad/s^2} is (retardation is uniform)

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