Calculating Rotation Rate from Change of Angle

[hidemi]

Homework Statement

A plane mirror is in a vertical plane and is rotating about a vertical axis at 100 rpm. A horizontal beam of light is incident on the mirror. The reflected beam will rotate at:

The answer is 200 rpm.

Relevant Equations

2θ = 2 dθ/dt

If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?

 

[collinsmark]

Homework Statement:: A plane mirror is in a vertical plane and is rotating about a vertical axis at 100 rpm. A horizontal beam of light is incident on the mirror. The reflected beam will rotate at:

The answer is 200 rpm.
Relevant Equations:: 2θ = 2 dθ/dt

If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?

Firstly, describe the reflected angle with respect to as a function of the angle of the plane.

Secondly, take the derivative.

[Edit: also, your "2θ = 2 dθ/dt" equation is incorrect.]

 

[hidemi]

Firstly, describe the reflected angle with respect to as a function of the angle of the plane.

Secondly, take the derivative.

[Edit: also, your "2θ = 2 dθ/dt" equation is incorrect.]

I got it. Thanks!

 

[Lnewqban]

The instantaneous angular velocity of the beam will be double, but it will take a minute to complete a full rotation, if I understand the problem correctly.
There will be no reflection while the mirror rotates between 90°and 270°