Question

prove that torque=dL/dt where is torque and L is angular momentum?​

Answer 1

Given,

l⃗ =r⃗ ×p⃗ dl⃗ /dt=ddt[r⃗ ×p⃗ ]

=dr⃗ /dt×p⃗ + r⃗ ×dp⃗ dt

Since,

dr⃗ /dt=v → and p⃗ =mv

The first term, m (v⃗ ×v⃗ )=0

Thus,

dl⃗ dt=0+r⃗ ×dp⃗ /dt=r⃗ ×dp/dt=r⃗ ×F⃗ =τ⃗

Therefore,

the time rate change in angular momentum is the torque.

dl⃗/ dt=τ⃗

Answer 2

Answer:

dL/dT= τ (τ = tow { A greek Alphabet} )

w.k.t

L= R x P

∴dL/dT=d(R x P)/dt

we also know that ;

d(A x B) / dT= dA/dT x A x B x dB/dT   (Applying this formula to the above                       equation we get;)

d(R x P) / dT = dR/dT x R x P x dP/dT

w.k.t;  dR/dT = v and dP/dT = F   ('F' is the force exerted)

∴ dL/dT = v x P + R x F

(P = m x v)

v x m x v + R x F= =dL/dT

(applying ; product of 2 vector quntity is "zero"

i.e. , A x A = 0 similarly, v x v = 0)

0 x m + R x F = dL/dT  [zero multiplied by anything is zero ]

(w.k.t ; R x F = τ)

∴ dL / dT = τ

Hence Proved

Explanation:

This is an important question from the chapter : "System of particles and Rotational motion" for 3 or 5 marks

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