AP Physics Review Rotational Motion

TOrque τ = Fd where d is the distance from the center of mass or pivot point (fulcrum) and F is the force perpendicular to d. Units are Nm If F is not perpendicular, then we can rewrite the equation as τ = Fd sin(Ɵ) This will use the perpendicular component of the force. Note that if the angle is 0 or 180, than there is no torque.

Net Torque In static equilibrium the sum of the forces = 0 and the sum of torques = 0. With forces we look at x and y directions and positivevs negative. With torque we look at clockwise vs counterclockwise.

Rotational Kinematics Remember that we use radians so ω has units of rad/s and α would be rad/s2 Same rules apply to these equations as we talked about with kinematics.

Moment Of Inertia Still refers to the objects resistance to changing motion. This deals with mass distribution. The further the mass is from the axis of rotation, the more inertia the object has and therefore will start rotating slower than an object of the same size and mass with mass concentrated at the axis. Units are kg m2 Ex. A bowling ball has less rotational inertia than a hollow sphere with the same mass because the mass of the bowling ball is evenly distributed while the hollow sphere will have all of its mass at the furthest distance from the axis as possible. For the moment of inertia of point the equation is: All other equations for different shapes will be provided.

Angular momentum Like linear momentum, angular momentum is also conserved. L = Iω Units are a kg m2/s. If the shape of the object or mass distribution changes then the angular velocity must adjust accordingly to conserve the momentum.