Question:
If the equation for the displacement of a particle moving on a circular path is given by $(\theta)=$ $2 t^{3}+0.5$ where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particleat $t = 2\, sec$, is
If the equation for the displacement of a particle moving on a circular path is given by $(\theta)=$ $2 t^{3}+0.5$ where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particleat $t = 2\, sec$, is
Updated On: Jul 5, 2022
- 24 rad/sec
- 12 rad/sec
- 8 rad/sec
- 36 rad/sec
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The Correct Option is A
Solution and Explanation
Angular velocity, $\omega=\frac{d \theta}{d t}=6 t^{2}$
at $t=2\, sec$
$w=6 \times 4=24\, rad / sec .$
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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.