Shortcut Methods
Shortcut Methods and Tricks to Solve Numerical Problems on Rotational Motion About a Fixed Axis
I. Kinematics
1. Uniform Circular Motion: To find the tangential velocity (v) of a point on the rim of a rotating disk, simply multiply the angular velocity (\omega) by the radius (r) of the disk.
$$v = \omega r$$
2. Uniform Angular Acceleration: To find the angular displacement (\theta) of a rotating wheel that starts from rest and accelerates uniformly, use the following formula:
$$ \theta = \frac{1}{2} \alpha t^2 $$
II. Dynamics
1. Rotational Kinetic Energy: To calculate the kinetic energy (K ) of a rotating disk or wheel, utilize the formula:
$$K= \frac{1}{2} I \omega^2$$
2. Angular Momentum: Determine the angular momentum (L ) of a rotating wheel, pulley, or other objects employing the equation:
$$ L = \frac{1}{2} m r^2 \omega $$
3. Tension in a String: For a rotating pulley with a mass attached to a string, apply the equation
$$T = m g - \frac{1}{2} mr^2\alpha$$
