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A. Explain what is the torque for the rotating body? b. If a 32.0 Nm torque on a wheel caused angular acceleration 25.0 rad/s², what is the wheel's rotational inertia (moment of inertia)?

Physics

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Here's the solution for question 11.b:

  1. Identify the given values and the unknown.

    Given:
    Torque, τ=32.0 Nm\tau = 32.0 \text{ Nm}
    Angular acceleration, α=25.0 rad/s2\alpha = 25.0 \text{ rad/s}^2
    Unknown:
    Rotational inertia (moment of inertia), II

  2. State the formula relating torque, moment of inertia, and angular acceleration.

    The relationship is given by Newton's second law for rotation:

    τ=Iα\tau = I \alpha

  3. Rearrange the formula to solve for the moment of inertia (II).

    I=ταI = \frac{\tau}{\alpha}

  4. Substitute the given values into the rearranged formula and calculate.

    I=32.0 Nm25.0 rad/s2I = \frac{32.0 \text{ Nm}}{25.0 \text{ rad/s}^2} I=1.28 kg m2I = 1.28 \text{ kg m}^2

    The wheel's rotational inertia is:

    1.28 kg m2\boxed{\text{1.28 kg m}^2}
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