Angular momentum preview

Angular momentum previews rotational conservation

A particle’s angular momentum about an origin measures how much its momentum is arranged to sweep area around that origin. Torque changes angular momentum just as force changes linear momentum.

Take the moment of Newton’s law

Define L = r × p. Differentiate: dL/dt = dr/dt × p + r × dp/dt. The first term is v × mv = 0, so dL/dt = r × F = τ. If external torque is zero, L is constant even if the particle’s speed and radius change.

A 0.2 kg mass moves at 5 m/s perpendicular to a radius of 0.4 m, so L = r m v = 0.4(0.2)(5) = 0.40 kg·m²/s. Halving r while conserving L doubles the tangential speed in an ideal central-force motion.

Angular momentum depends on the chosen origin

The same motion can have zero angular momentum about a point on its line of motion and nonzero angular momentum about a displaced point. State the origin before comparing values.

Work it: A 1 kg puck travels at 3 m/s along a line 0.5 m from the origin. Find angular momentum magnitude and the torque needed to change it by 2 kg·m²/s in 4 s.