12th HSC Physics - Rotational Dynamics Formula Sheet
1. Angular Kinematics
theta = omega * t + (1/2) * alpha * t^2
omega = omega_0 + alpha * t
omega^2 = omega_0^2 + 2 * alpha * theta
2. Relation Between Linear and Angular Quantities
s = r * theta
v = r * omega
a_t = r * alpha
a_c = v^2 / r = r * omega^2
3. Moment of Inertia (I)
Point mass: I = m * r^2
Standard Bodies:
Ring (central axis): I = M * R^2
Disc (central axis): I = (1/2) * M * R^2
Solid Sphere (diameter): I = (2/5) * M * R^2
Hollow Sphere: I = (2/3) * M * R^2
Rod (center): I = (1/12) * M * L^2
Rod (end): I = (1/3) * M * L^2
1. Angular Kinematics
theta = omega * t + (1/2) * alpha * t^2
omega = omega_0 + alpha * t
omega^2 = omega_0^2 + 2 * alpha * theta
2. Relation Between Linear and Angular Quantities
s = r * theta
v = r * omega
a_t = r * alpha
a_c = v^2 / r = r * omega^2
3. Moment of Inertia (I)
Point mass: I = m * r^2
Standard Bodies:
Ring (central axis): I = M * R^2
Disc (central axis): I = (1/2) * M * R^2
Solid Sphere (diameter): I = (2/5) * M * R^2
Hollow Sphere: I = (2/3) * M * R^2
Rod (center): I = (1/12) * M * L^2
Rod (end): I = (1/3) * M * L^2
