Question:
A constant torque of $ 3.14\,Nm $ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $ 4\pi \,rad/s^{2}, $ then the moment of Inertia of the wheel is
A constant torque of $ 3.14\,Nm $ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $ 4\pi \,rad/s^{2}, $ then the moment of Inertia of the wheel is
Updated On: May 15, 2024
- $ 0.25\,kg-m^{2} $
- $ 2.5\,kg-m^{2} $
- $ 4.5\,kg-m^{2} $
- $ 25\,kg-m^{2} $
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The Correct Option is A
Solution and Explanation
Torque, $ \tau =I\omega $
Moment of inertia, $ I=\frac{\tau }{\omega } $
$ =\frac{3.14}{4\times \pi } $
$ =\frac{3.14}{4\times 3.14}=\frac{1}{4} $
$ =0.25\,kg-m^{2} $
Moment of inertia, $ I=\frac{\tau }{\omega } $
$ =\frac{3.14}{4\times \pi } $
$ =\frac{3.14}{4\times 3.14}=\frac{1}{4} $
$ =0.25\,kg-m^{2} $
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.