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A constant torque of 1000 N-m turns a wh...

A constant torque of `1000 N-m` turns a wheel of moment of inertia `200 kg-m^2` about an axis through its centre. Its angular velocity after `3` seconds is.

A

`1 rad//s`

B

`5 rad//s`

C

`10 rad//s`

D

`15 rad//s`

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The correct Answer is:
To find the angular velocity of the wheel after 3 seconds under the influence of a constant torque, we can use the following steps: ### Step 1: Understand the relationship between torque, moment of inertia, and angular acceleration. The relationship is given by Newton's second law for rotation: \[ \tau = I \alpha \] where: - \(\tau\) is the torque, - \(I\) is the moment of inertia, - \(\alpha\) is the angular acceleration. ### Step 2: Calculate the angular acceleration (\(\alpha\)). Rearranging the equation gives us: \[ \alpha = \frac{\tau}{I} \] Substituting the given values: \[ \alpha = \frac{1000 \, \text{N-m}}{200 \, \text{kg-m}^2} = 5 \, \text{rad/s}^2 \] ### Step 3: Use the angular acceleration to find the final angular velocity (\(\omega\)). The angular velocity after a time \(t\) can be calculated using the formula: \[ \omega = \omega_0 + \alpha t \] where: - \(\omega_0\) is the initial angular velocity (which is 0 since the wheel starts from rest), - \(t\) is the time in seconds. Since the wheel starts from rest, \(\omega_0 = 0\): \[ \omega = 0 + (5 \, \text{rad/s}^2)(3 \, \text{s}) = 15 \, \text{rad/s} \] ### Final Answer: The angular velocity of the wheel after 3 seconds is \(15 \, \text{rad/s}\). ---

To find the angular velocity of the wheel after 3 seconds under the influence of a constant torque, we can use the following steps: ### Step 1: Understand the relationship between torque, moment of inertia, and angular acceleration. The relationship is given by Newton's second law for rotation: \[ \tau = I \alpha \] where: ...
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Knowledge Check

  • A costant torque of 400 N turns a flywheel at rest and of "M.I. 100 kgm"^(2) about an axis through its centre. What is the change in its angular velocity in 4 s?

    A
    8 rad/s
    B
    12 rad/s
    C
    16 rad/s
    D
    20 rad/s
  • A torque of 30 N-m is acting on a wheel of mass 5 kg and moment of inertia 2 kg-m​^(2) ​. If wheel starts rotating from rest then its angular displacement in 10 seconds will be-

    A
    750rad
    B
    1500rad
    C
    300rad
    D
    6000rad
  • The moment of inertia of ring about an axis passing through its diameter is I . Then moment of inertia of that ring about an axis passing through its centre and perpendicular to its plane is

    A
    `2I`
    B
    `I`
    C
    `I//2`
    D
    `I//4`
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