Rigid body rotating around a point A Linear motion

Rotational angular momentum Let’s look at the bicycle wheel again. What is the total angular momentum of the wheel around its center of mass? ω

Rotational angular momentum Let’s look at the bicycle wheel again. What is the total angular momentum of the wheel around its center of mass? ω

Rotational angular momentum Let’s look at the bicycle wheel again. What is the total angular momentum of the wheel around its center of mass? ω The rotational angular momentum of a rigid body around its center of mass:

Rotational angular momentum Let’s look at the bicycle wheel again. What is the total angular momentum of the wheel around its center of mass? ω The rotational angular momentum of a rigid body around its center of mass: (If the body is planar, or symmetrical around its axis of rotation.) 对称的

Example: A thin rod of mass M and length L has two small balls of mass m stuck to its ends. The system rotates around its center of mass with angular speed ω. What is the rotational angular momentum (around the center of mass)? ω M m m L ω

M m m L ω Example: What happens if we move the axis of rotation here? Find the total angular momentum (around the new center of rotation). ω

Three fundamental principles Momentum principle Energy principle ?.......

Angular momentum principle Greek letter “tau” Instantaneous version: where is the torque (力矩) around the point A.

Torque …and much easier here, further from the hinges. It is hard to close the door by pushing here…

Calculating torque: method 1 Direction of torque from right-hand rule. The component of the force perpendicular to r is F sin φ. Then

Calculating torque: method 2 “lever arm”

Calculating torque: method 3 Magnitude:

Example

Example

Example