a grindstone of mass 40 kg has a radius of 1.2m. Starting from rest it acquires a speed of 150 rpm in 12 seconds. Calculate the torque acting on it
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Answer: 6 Nm
Explanation:
Given,
mass, m = 40 kg
radius, r = 1.2 m
angular speed, w =150 rpm
= 150/60 rps
= 2.5 rps
time taken to obtain angular speed w, t= 12 sec
Now,
angular acceleration, α = w/t
= 2.5/ 12
Moment of inertia of the grind stone( which is a disc at its centre of mass), I = 1/2 mr^2
= 1/2 × 40 × 1.2 × 1.2
Now,
Torque acting on the grind stone
= moment of inertia * angular acc^n
= I × α
= (1/2)×40×1.2×1.2×(2.5/12)
= 6 Nm.
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