A friction pully has the shape of a uniform solid disk of mass 2.50kg and radius

Question

A friction pully has the shape of a uniform solid disk of mass 2.50kg and radius 20.0cm. A 1.50 kg stone is attached to a very light wire that is wrapped around the rim of the pully and the system is released from rest. The moment value is on the last page. What is the relationship between the disc angular speed and the stone descending speed (Elucidate in formula. When the stone descends. 2.00m height, what is the speed of the stone. What is the angular speed of the pully in condition of b

Explanation / Answer

(a)When stone descend then stone potential energy will get converted into the kinetic energy.
So at any moment the kinetic energy attained by the stone will be equal to the kinetic energy of the disc pulley.
therefore
(1/2)mV2 = (1/2)IW2
where m is the mass of stone and V is the velocity , I is the moment of inertia and W is the angular velocity of Pulley
I = MR2 /2 = 2.5*(0.2)2 /2 = 0.05 where M is the mass of the pulley and R is the radius .
now putting all the values
(1/2)*1.5V2 = (1/2)*0.05*W2
V = 0.1826 W
(b)
When stone descend 2 m then
mgh = (1/2)mV2
V = (2gh)1/2 = (2*9.81*2)1/2 = 6.264 m/s
And W = 1.144 rad/s

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