Torque, Momentum and Reflection

In summary, the angular acceleration of a mirror of length L and mass m, hit by a light beam with frequency f at a distance 3/4 L from one end and reflecting at a rate of N photons per second, can be found using the formula γ = (9/2) Nhf/McL.
  • #1
jaumzaum
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A light beam of frequency f hits a mirror of length L at a distance 3/4 L from one end, which is fixed but can rotate freely around the axis as shown. The mirror has mass m and can be considered a rectangular plate. The light beam hits (and fully reflects) the mirror at a rate of N photons per second. Find the angular acceleration of the mirror.


I did this, can anyone tell me if it's right?

The moment of inertia of the mirror is I = ML²/3
The linear momentum of the beam is p = hf/c

The variation of the linear momentum in function of time is 2Nhf/c = F (where F is the force exerted on the mirror)

The torque T = F.(3/4L) = (3/2) NhfL/c = Iγ = (ML²/3) γ
γ = (9/2) Nhf/McL
 
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  • #2
The linear momentum of the beam is p = hf/c
You mean photon, not beam, but otherwise looks ok.
 

1. What is torque and how is it related to force?

Torque is a measure of the twisting force on an object. It is directly related to force through the equation torque = force x distance, where distance is the shortest distance from the axis of rotation to the point where the force is applied.

2. How does momentum differ from velocity?

Momentum is a measure of the quantity of motion an object has, while velocity is a measure of the speed and direction of an object's motion. Momentum takes into account the mass and velocity of an object, while velocity only considers the speed and direction.

3. How does reflection occur?

Reflection is the change in direction of a wave or particle when it encounters a boundary or obstacle. This change in direction is due to the wave or particle bouncing off the surface, with the angle of incidence equal to the angle of reflection.

4. What is the difference between elastic and inelastic collisions?

In an elastic collision, both the momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the objects before and after the collision are equal. In an inelastic collision, only momentum is conserved, and some kinetic energy is lost in the form of heat or sound.

5. How is torque used in everyday life?

Torque is used in everyday life in many different ways, such as opening a door, tightening a bolt, or riding a bike. It is also important in machines and vehicles, where it is used to generate motion and power. In sports, torque is used in throwing, swinging, and kicking movements.

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