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17 October, 16:47

You have a grindstone (a disk) that is 95.2 kg, has a 0.399 m radius, and is turning at 93 rpm, and you press a steel axe against it with a radial force of 19.6 N. (a) Assuming the kinetic coefficient of friction betweensteel and stone is 0.2, calculate the angular acceleration of thegrindstone.

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  1. 17 October, 17:00
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    angular acceleration is - 0.2063 rad/s²

    Explanation:

    Given data

    mass m = 95.2 kg

    radius r = 0.399 m

    turning ω = 93 rpm

    radial force N = 19.6 N

    kinetic coefficient of friction μ = 0.2

    to find out

    angular acceleration

    solution

    we know frictional force that is = radial force * kinetic coefficient of friction

    frictional force = 19.6 * 0.2

    frictional force = 3.92 N

    and

    we know moment of inertia that is

    γ = I * α = frictional force * r

    so

    γ = 1/2 mr²α

    α = - 2f / mr

    α = - 2 (3.92) / 95.2 (0.399)

    α = - 7.84 / 37.9848 = - 0.2063

    so angular acceleration is - 0.2063 rad/s²
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