(455) HL Angular momentum and impulse [IB Physics HL]

Angular Momentum

• Defined as the rotational equivalent of linear momentum.

• Equation: L = I \Omega

  • Where L = angular momentum, I = moment of inertia, \Omega = angular velocity.

• Units:

  • Angular velocity (\Omega) in radians per second.

  • Moment of inertia (I) calculated as Σmr² (kg·m²).

  • Thus, angular momentum (L) is expressed in kg·m²/s (radians often omitted).

Conservation of Angular Momentum

• Angular momentum is conserved when there are no external net torques.

• Total angular momentum (L) remains constant if no external forces act on the system.

• Key relationship: If radius (r) increases, angular velocity (\Omega) decreases, and vice versa.

  • Example: A spinning figure skater pulls arms in (r decreases), causing rotation speed (\Omega) to increase.

Real-World Example

• The Crab Nebula and its neutron star spun faster after a supernova explosion, illustrating the conservation of angular momentum on a cosmic scale.

• The star collapses, decreasing radius, resulting in increased angular velocity (30 times per second). This neutron star is observed as a pulsar.

Angular Impulse

• Analogous to linear impulse, represented as J for angular impulse.

• Equation: J = ΔL = τ \Delta T

  • Where τ = torque, ΔT = change in time.

• Change in angular momentum (ΔL) equals angular impulse (J).

Summary

• Explored angular momentum, conservation principles, real-world examples (figure skaters, neutron stars), and introduced angular impulse as the rotational equivalent of linear impulse.