# Need help with Newtonian equations with angular momentum

For an equations such as this what goes into the θ?

θ = sinθ or θ = θ?

Let's say if the angle of displacement = 45° do I just plug 45° as θ into the equation below or should it be sin(45°)?

Or is it θ = S/R ?
ωf2 = ωi2 + 2 α (θf - θi)

Last edited:

Simon Bridge
Homework Helper
There is no way of knowing without the specific problem you are trying to solve.

##\theta = \sin\theta## is true for the intersection of the line ##y=\theta## with the curve ##y=\sin\theta## which occurs for ##\theta=0##
The relation ##\sin\theta \approx\theta## is known as the par-axial approximation, it applies when ##\theta \approx 0##.

If you want to find the arclength subtended by 45 degrees, then you would put ##\theta = \frac{\pi}{4}## into ##S=R\theta## to find out.

If an object has turned through 45deg starting with speed ##\omega_i## and accelerating at constant ##\alpha## ... and you wanted to know the final angular velocity, then you would put ##\theta = \frac{\pi}{4}## into ##\omega_f^2=\omega_i^2+2\alpha\theta##

It is unclear what you mean by "the Newtonian equations" in this context ... Newton's second law, for instance, would be ##\sum\vec \tau = I\vec\alpha##

In physics: angles are always used in radians, and you should never try to work a physics problem just by putting numbers into equations: you should use physics to find the equation first.