Insane physics homework...I need help!?

Question

Given an object in constant circular motion, at a radius of r with (angle) = (omega) (times) t, apply rectangular conversion of polar coordinates and differential calculus to derive the perimeter speed and the scalar acceleration of the object.

Answer 1

x = r cos(θ) = r cos(ωt)
y = r sin(θ) = r sin(ωt)

The x-component of the velocity vector is dx/dt = -rω sin(ωt)
The y-component of the velocity vector is dy/dt = rω cos(ωt)

The speed, which is the magnitude of the velocity, is the square root of the sum of the squares of the x- and y-components of the velocity vector. You should get rω.

Similarly,

the x-component of the acceleration vector is d²x/dt² = -rω² cos(ωt)
the y-component of the acceleration vector is d²y/dt² = -rω² sin(ωt)

The scalar acceleration, which is the magnitude of the acceleration vector, is the square root of the sum of the squares of the x- and y-components of the acceleration vector. You should get rω².