Fixed-Axis Rotation (Physics)

Recall cards on the rotation of a rigid body about a fixed axis. Rotational variables: angular position theta = s/r in radians, angular displacement, angular velocity omega = d theta/dt, and angular acceleration alpha = d omega/dt, with the counterclockwise-positive sign convention and the right-hand rule for the direction of the angular velocity vector. Rotation with constant angular acceleration: the four rotational kinematic equations as direct analogs of the linear ones (theta for x, omega for v, alpha for a). Relating angular and translational quantities: tangential speed v_t = r omega, tangential acceleration a_t = r alpha, centripetal acceleration a_c = r omega^2, and the total linear acceleration. Moment of inertia and rotational kinetic energy: K = (1/2) I omega^2, I = sum m r^2 as the rotational analog of mass, and its dependence on the axis and the mass distribution. Calculating moments of inertia: the integral I = integral r^2 dm, the parallel-axis theorem I = I_cm + m d^2, and standard results for a rod (about center and end), a disk, and compound bodies. Torque tau = r x F, its magnitude r F sin theta, the lever arm, net torque, and its sign. Newton's second law for rotation, sum tau = I alpha, the rotational analog of F = ma. And work and power for rotational motion, W = integral tau d theta, the work-energy theorem, and P = tau omega.