Exercise 1

We start with equations (3) from Lecture 2: \[ a_x = -R \omega^2 \cos \omega t \] \[ a_y = -R \omega^2 \sin \omega t \]

and compute the magnitude of the acceleration: \[ a = \sqrt{a_x^2 + a_y^2} \]

If we plug this in, we get: \[ a = \sqrt{R^2 \omega^4 \cos^2 \omega t + R^2 \omega^4 \sin^2 \omega t} \] \[ = \sqrt{R^2 \omega^4 (\cos^2 \omega t + \sin^2 \omega t) } \] \[ = \sqrt{R^2 \omega^4} \] \[ = R \omega^2 \]