Spinning, Twisting, and Turning

Rotational motion deals with objects that spin or rotate, from wheels to planets. Instead of linear displacement and force, we use angular displacement and torque.

Key Quantities

• Angular Displacement (\( \theta \)): How much something turns, measured in radians.
• Angular Velocity (\( \omega \)): How fast it's spinning.
• Angular Acceleration (\( \alpha \)): How quickly the spin rate changes.
• Torque (\( \tau \)): The rotational equivalent of force.

Rotational Equations

The rotational version of Newton's second law is: \[ \tau = I\alpha \] where \( I \) is the moment of inertia, a measure of how mass is distributed around the axis.

Applications

From opening doors to spinning figure skaters, torque and rotational motion are everywhere!