Question

A rotating source of light throws a beam of light onto a screen  Point P on the screen should move with constant velocity v₀. Determine the required angular acceleration ¨ϕ(ϕ) of the source of light. Sketch ˙ϕ(ϕ) and ¨ϕ(ϕ).

Answer 1

The position of point P is given by 

x =r₀tanϕ 

0 tanϕ . We write down the inverse function 

ϕ = arctanx/r₀

 Differentiation with ˙x = v = v₀ = const yeilds

Note: the maximum value of ¨ϕ, located at ϕ = ±30◦ , is obtained as