g A has all the mass at the rim, while wheel B has the mass uniformly distributed, like a solid disk. The wheels have the same mass. The sam

Question

g A has all the mass at the rim, while wheel B has the mass uniformly distributed, like a solid disk. The wheels have the same mass. The same torque is applied to both wheels. Which one accelerates faster in response to this torque?

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Thu Giang 6 months 2021-07-20T20:28:29+00:00 2 Answers 2 views 0

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    0
    2021-07-20T20:29:39+00:00

    Answer:

    The rim accelerates faster than the disk in response to the torque.

    Explanation:

    Given:

    For the rim:

    mass = M

    radius = R

    The moment of inertia is:

    I_{A} =MR^{2}

    For the disc:

    mass = M

    radius = 2R

    The moment of inertia is:

    I_{B} =\frac{1}{2} M(2R)^{2} =2MR^{2}

    If the same torque is applied, thus:

    \tau _{A} =\tau _{B} \\I_{A}\alpha  _{A} =I_{B}\alpha  _{B} \\MR^{2}\alpha  _{A}=2MR^{2}\alpha  _{B} \\\alpha  _{A}=2\alpha  _{B}

    According to this result, the rim accelerates faster than the disk.

    0
    2021-07-20T20:30:00+00:00

    Answer:

    The second wheel

    Explanation:

    The torque is given by

    \tau=I\alpha   (1)

    where I is the moment of inertia and a is the angular acceleration. If we take into account the moment of inertia of a disk and a ring ()for the first wheel) we have:

    I_r=mR^2\\I_d=\frac{1}{2}mR^2

    where we used that both wheel have the same mass. By replacing in (1) we obtain:

    \alpha_r=\frac{\tau}{I_r}=\frac{\tau}{mR^2}\\\alpha_d=\frac{\tau}{I_d}=\frac{\tau}{\frac{1}{2}mR^2}=2\alpha_r\\

    Hence, the second wheel (the disk) has a greater acceleration.

    hope this help!!

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