Calculating Rotation Rate from Change of Angle

AI Thread Summary
The discussion centers on calculating the rotation rate of a reflected beam of light from a rotating mirror. It is established that if the mirror rotates at 100 rpm, the reflected beam rotates at 200 rpm due to the change of angle being twice the incident angle. Participants clarify the need to describe the reflected angle as a function of the mirror's angle and take its derivative for a better understanding. An error in the equation "2θ = 2 dθ/dt" is noted, prompting further explanation. The conclusion emphasizes that the reflected beam's instantaneous angular velocity is double that of the mirror, with no reflection occurring between 90° and 270°.
hidemi
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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?
 
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hidemi said:
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.]
 
collinsmark said:
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!
 
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°
 
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