A block hangs from a string wrapped on a disc of radius 20 cm free to rotate about its axis which is fixed in a horizontal position. If the angular speed of the disc is 10 rad/s at some instant, with what speed is the block going down at that instant?

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Solution

It is given that the string is moving on the rim of the disc and block is connected with the string.
Therefore, the speeds of the block going down and the rim will be same.
Angular speed of the disc, ω = 10 rad/s
Radius of the pulley, r = 20 cm

Linear velocity of the rim, v = Tangential velocity = rω
v = 10 × 20 = 200 cm/s = 2 m/s
Therefore, velocity of the block = 2 m/s

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