10-31-25 Rotational Angular Momentum

Angular Momentum

  • Along with momentum and energy, angular momentum is a fundamental quantity that helps us to predict motion

  • We will see how angular momentum is associated with translational and rotational motion

Direction of Rotation: Angular Velocity

  • The vector direction associated with a rotation is always along the direction of the axis of rotation. The specific direction is determined by the curling of the motion around the axis, through use of the ‘right hand rule’

Rotational Angular Momentum

  • For a rigid object rotating around its center of mass, the rotational angular momentum is given by:

\overrightarrow L_{rot} = I_{cm} \overrightarrow \omega

  • The direction of the angular velocity is also given by the right hand rule:

A wheel is rotating as shown in the picture below. What is the direction of the rotational angular momentum of the wheel?

A) +x 

B) +y

C) +z
D) -x

E) -y

F) -z

Use the right hand rule. 

The answer is D

A diatomic molecule such as molecular nitrogen (N_2) consists of two atoms each of mass m, whose nuclei are a distance d apart. The molecule rotates with an angular speed \omega around its center of mass. What is the magnitude of the rotational angular momentum of this molecule?

A) md²\omega²

B) 2md²\omega

C) \frac 12 md²\omega

D) \frac 14 md²\omega

E) 4md²\omega

\overrightarrow L_{rot} = I_{cm} \overrightarrow\omega

\Rightarrow \overrightarrow L_{rot} = (\frac 12 \cdot md²) (\overrightarrow \omega)

The answer is C