Asked Nov 5, 2019

You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius,
and is turning at 90.0 rpm, and you press a steel axe against it with a
radial force of 20.0 N. (a) Assuming the kinetic coefficient of friction
between steel and stone is 0.20, calculate the angular acceleration of
the grindstone. (b) How many turns will the stone make before coming
to rest?


Expert Answer

Step 1

Consider the mass of the grindstone be m, the radius of the grindstone disk be r, the normal reaction on the grindstone disk by steel, that equals to the radial force, be N, the grindstone disk’s moment of inertia be I, the frictional force between the grindstone disk and steel be Ff, and the angular acceleration of the grindstone be α.


Write the expression for the torque produced by the frictional force.


Image Transcriptionclose

r(r)(F,)-(r)(4,N) (r)(4F) =(0.340 m) (0.20(20.0 N)) 1.36 N.m

Step 2



Write the expression for the torque in terms of the moment of inertia of the grind...


Image Transcriptionclose

27 mr2 1 mr I 2(1.36 N m) 2 (90.0 kg)(0.340 m) 1 kg m/s 2.72 N 1N 10.404 kg m 0.261 rad/s2


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Angular Motion

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