Question

angular momentum,L= rp, then torque = dL/dt. find value of torque​

Answer 1

Answer:

Assume a particle has angular velocity ω about a pivot point. We define the angular momentum L of the particle about the point as L = r × p, where r is the displacement vector of the particle from the pivot point and p is its momentum. The direction of L is perpendicular to both r and p.

Let r and p lie in the x-y plane, as shown in the figure on the right.

Then L = r p sinθ k. For a particle moving in a circular path sinθ = 1,

L = r p k = r m v k = mr2ω k = Iω,

since ω = ωk and the moment of inertial of te particle about the pivot point is mr2.

L = Iω.

The change in angular momentum of the particle is

dL/dt = d(r × p)/dt = r × dp/dt + dr/dt × p.

The last term on the right is proportional to v × vand therefore is zero. We have

dL/dt = r × dp/dt = r × F = τ.

τ = dL/dt is the rotational analog of Newton's second law, F = dp/dt.