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A constant torque is acting on a wheel. ...

A constant torque is acting on a wheel. If starting from rest, the wheel makes n rotations in t seconds, show that the angular
acceleration is given by `alpha = (4pi n)/(t^(2)) rad s^(-2)`.

Text Solution

Verified by Experts

Here, `omega_(1) = 0`. Number of rotations in `t sec = n`
`:.` angular displacement, `theta = 2pi n`
As `theta = omega_(1) r + (1)/(2) alpha t`
`:. 2pi n = 0 + (1)/(2) alpha t^(2), alpha = (4pi n)/(t^(2)) rad//s^(2)`
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Knowledge Check

  • On the application of a constant torque , a wheel is turned from rest through 400 radians in 10 s. The angular acceleration is :

    A
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    B
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  • A torque of 50 N-m acting on a wheel at rest rotates it through 200 rad in 5 sec. Its angular acceleration is -

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    B
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    C
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    D
    `20" "rad//s^(2)`

  • A torque of 100 Nm acting on a wheel at rest, rotates it through 200 radians in 10 s. The angular acceleration of the wheel, in rad//s^(2) is

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