Derivation Of Newton's Second Law For Rotations
Let ri, pi, li and Fneti denote the displacement, linear momentum, angular momentum and net force for particles in a system for i = 1, 2, 3, ..., N:
L = l1 + l2 + l3 + ... + lN = r1 x p1 + r2 x p2 + r3 x p3 + ... + rN x pN
L' = l'1 + l'2 + l'3 + ... + l'N = r1 x Fnet1 + r2 x Fnet2 + r3 x Fnet3 + ... + rN x FnetN
Therefore, the net torque on a system of particles equals its angular momentum derivative.
L = l1 + l2 + l3 + ... + lN = r1 x p1 + r2 x p2 + r3 x p3 + ... + rN x pN
L' = l'1 + l'2 + l'3 + ... + l'N = r1 x Fnet1 + r2 x Fnet2 + r3 x Fnet3 + ... + rN x FnetN
Therefore, the net torque on a system of particles equals its angular momentum derivative.
Comments
Post a Comment