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What constant torque should be appiled t...

What constant torque should be appiled to a disc of mass `10 kg` and diameter `50 cm` so that it acquires an angular velocity of `2pi` rad/s in `4 s` ? The disc is initially at rest and rotates about an axis through the centre of the disc and in a plane perpendicular to the disc.

Text Solution

Verified by Experts

Here, `tau = ? M = 10 kg`,
`R = (50)/(2) cm = (1)/(4)m`
`omega = 2pi rad//s, t = 4 s, omega_(0) = 0`.
Moment of inertia of disc about the given axis
`I = (1)/(2)MR^(2)`
`alpha = (omega - omega_(0))/(t) = (2pi - 0)/(4) = (pi)/(2) rad//s^(2)`
`tau = I alpha = (1)/(2) MR^(2) xx (pi)/(2)`
`= (pi)/(4) xx 10 ((1)/(4))^(2) = (110)/(224) = 0.49 N-m`
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