Question

A ring of mass m and radius R which is free to rotate about its axis, is at rest at t = 0. A constant force F is applied to it tangentially. What will be the angular momentum of the ring after t seconds?
1. mR²t
2. Ft
3. FRt
4. \(\frac{Ft}{R}\)

Answer 1

Correct Answer - Option 3 : FRt

Concept:

Rotational motion:

•  When a block is moving about a fixed axis on a circular path then this type of motion is called rotational motion.
• Torque (τ): It is the twisting force that tends to cause rotation.
  • The point where the object rotates is known as the axis of rotation. 
• Mathematically it is written as,

⇒ τ = r F sin θ 

Where r is the distance between the axis of rotation and point of application of force, F is force and θ is the angle between r and F.

Angular Momentum:

• It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is a vector quantity

​⇒ L = Iω

where I = moment of inertia and ω = angular velocity. 

Just as a force is defined as the rate of change of momentum, torque is defined as rate of change of angular momentum. 

Calculation:

Given, mass of ring M

Radius R

time t

Force F

Torque τ = F R

Angular momentum L (Let)

τ = L / t

​⇒ L = τt = FRt

So, the correct option is FRt.