Question

A body of mass ‘m’ is moving with a velocity ‘V” about an axis at a distance of T from the axis.

1. How is its linear velocity related with angular velocity?

2. Derive the relation connecting torque and angular momentum.

Answer 1

1. Relation between linear velocity and angular velocity is (\vec v = \vec ω \times \vec r) where V is the linear velocity and co is the angular velocity and r is the radius of rotation.

2. We know (\vec L = \vec ω \times \vec p.....(1))

where, L is angular momentum, r is radius of rotation and p is linear momentum of the particle. Differentiating (1) with respect to time,

Thus torque is rate of change of angular momentum.