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Question

A grindstone in the shape of a solid disk with diameter 0.520 m and a mass of 50.0 kg is rotating at 850 rev/min . You press an axe against the rim with a normal force of 160 N (see the figure below), and the grindstone comes to rest in 7.00 s. (Figure 1) Part A Find the coefficient of kinetic friction between the axe and the grindstone. There is negligible friction in the bearings.

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Answer “A grindstone in the shape of a solid disk with diameter 0.520 m and a mass of 50.0 kg is rotating at 850 rev/min”.

Physics of Rotational Motion:

Rotating Objects: The torque that is applied to an object in the direction of angular speed is equal to the multiplicative of moment of inertia and the object’s angular acceleration around the axis.

That is:

Where τ is a resultant torque on the rotating objects about the direction of rotation, I represents the moment of inertia and α represents the angular acceleration around the axis.

Answer and Explanation:

Given:

Radius from the grindstone is:  R=0.520/2  m=0.260 m

The mass of the grindstone is: M=50 kg

The initial angular acceleration of the grindstone is 

The grindstone’s final angular acceleration is

The usual force on the grindstone: N = 160N

Time taken by the grindstone to comes to rest is t = 7s

The dynamics of rotation dictates that,

The moment of inertia of the grindstone is:

The law of rotation:

The frictional force can be compared to the normal force component as follows

The coefficient of kinetic friction between the grindstone and the axe is µ_k = 0.0131

Last words

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