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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

AI Generated Solution

To solve the problem, we need to find the angular acceleration (\( \alpha \)) of a wheel that starts from rest and makes \( n \) rotations in \( t \) seconds under the influence of a constant torque. ### Step-by-Step Solution: 1. **Understand the problem**: The wheel starts from rest, which means the initial angular velocity (\( \omega_0 \)) is 0. We are given the number of rotations (\( n \)) and the time taken (\( t \)). 2. **Convert rotations to radians**: Since one rotation corresponds to \( 2\pi \) radians, \( n \) rotations will correspond to: \[ ...
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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
    `8 rad s^(-2)`
    B
    `5 rad s^(-2)`
    C
    `6 rad s^(-2)`
    D
    `7 rad s^(-2)`
  • A torque of 50 N-m acting on a wheel at rest rotates it through 200 rad in 5 sec. Its angular acceleration is -

    A
    `0.16rad//s^(2)`
    B
    `1.6rad//s^(2)`
    C
    `16rad//s^(2)`
    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

    A
    2
    B
    4
    C
    1
    D
    8
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