1.

Show that dl/dt = τ, where L is the angular momentum and τ is the torque.​

Answer»

As we know, L = r × p, differentiating on both the SIDES,

⇒ \frac{dl}{dt}

dt

dl

= \frac{d}{dt}

dt

d

( r × p)

⇒ \frac{dl}{dt}

dt

dl

= \frac{dr}{dt}

dt

dr

× p + r × \frac{dp}{dt}

dt

dp

⇒ \frac{dl}{dt}

dt

dl

= v × p + r × \frac{dp}{dt}

dt

dp

⇒ \frac{dl}{dt}

dt

dl

= v × MV + r × \frac{dp}{dt}

dt

dp

SINCE, v = 0

⇒ \frac{dl}{dt}

dt

dl

= r × \frac{dp}{dt}

dt

dp

= r × F = τ

⇒ \frac{dl}{dt}

dt

dl

= τ


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