A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a

Question

A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim

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Verity 3 years 2021-08-31T04:31:05+00:00 2 Answers 384 views 0

Answers ( )

  1. vankhanh
    0
    2021-08-31T04:32:12+00:00
    Reply

    Answer:

    v=2.45 m/s

    Explanation:

    The rotational kinetic energy is calculated with:

    K=\frac{I\omega^2}{2}

    The moment of inertia of a disk is:

    I=\frac{mr^2}{2}

    A point on the rim of a disk will have a speed of:

    v=r\omega

    Putting all together:

    v=r\sqrt{\frac{2K}{I}}=r\sqrt{\frac{2(2K)}{mr^2}}=2\sqrt{\frac{K}{m}}

    Which for our values is:

    v=2\sqrt{\frac{0.15J}{0.1Kg}}=2.45m/s

  2. kimcuc
    0
    2021-08-31T04:33:00+00:00
    Reply

    Given Information:

    kinetic energy = E = 0.15 J  

    mass = m = 100g = 0.1 kg

    diameter = d = 8.0 cm = 0.08 m

    Required Information:

    Speed = v = ?

    Answer:

    v = 2.44 m/s

    Explanation:

    First convert diameter into radius

    r = d/2 = 0.08/2 = 0.04 m

    The moment of inertia of disc is given by

    I = 0.5mr²

    Where m is the mass and r is the radius of the disk

    I = 0.5(0.1)(0.04)²

    I = 0.00008 kg.m²

    and since we are dealing with rotational motion then rotational kinetic energy is given by

    E  =  0.5 I ω²

    we have to separate ω

    ω² = E/0.5 I

    ω = √E/0.5 I

    ω = √0.15/0.5(0.00008)

    ω = 61.23 rad/sec

    Finally we know that speed is given as

    v = ω r

    v = 61.23 (0.04)

    v = 2.44 m/s

    Therefore, the speed of a point on the rim  is 2.44 m/s

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