Introduction to Rotational Motion | You'll Remember This Even After 7 Lives

Rigid Bodies and Modes of Motion On an inclined plane, a hollow sphere, a solid sphere, a hollow cylinder, a solid cylinder, and a frictionless cube—all of the same mass and size—are released together, raising the question of which arrives first. Rotational motion, unlike the circular motion of a point mass, concerns extended rigid bodies whose internal distances remain fixed under applied forces. In pure translation, every point moves the same amount and direction, so any internal line remains parallel to its original orientation. In pure rotation about a fixed axis, each point traces a circle with the same angular velocity and angular acceleration while linear speeds vary, and internal lines change orientation. Rolling combines both: the center of mass translates while the body’s points simultaneously rotate about it.

Torque: Force, Distance, and Angle Torque—the turning effect that causes rotation—depends on the applied force, its distance from the axis, and the angle between the force and the position vector: tau = r F sin(theta). Pushing at a door’s hinge gives zero torque, whereas pushing farther from the hinge makes it open easily. Direction matters: anticlockwise torque is positive and clockwise negative, and in vector form torque = r cross F points perpendicular to the plane of rotation. Torque produces angular acceleration according to tau = I alpha.