Show that dl/dt = τ, where L is the angular momentum and τ is the torque.
Answers
Answered by
1
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
Similar questions
Hindi,
1 month ago
Social Sciences,
1 month ago
Math,
1 month ago
Math,
11 months ago
English,
11 months ago