Kinematics of Circular Motion: Practice Problem & Solution
A rigid body rotates about a stationary axis according to the equation, \(\theta = 6t^2 - 2t^3\). Its angular velocity, when its angular acceleration becomes 6 \(\text{rad/s}^2\), will be (Where \(\theta\) denotes angular displacement in radian, t denotes time in second)
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Kinematics of Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:
Angular velocity is \(omega = 12t - 6t^2\) and angular acceleration is \(alpha = 12 - 12t\). Setting \(alpha = 6\text{ rad/s}^2\) gives \(t = 0.5\text{ s}\). Thus, \(omega = 12(0.5) - 6(0.5)^2 = 4.5\text{ rad/s}\).
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