A very thin circular hoop of mass m and radius r rolls without slipping down a ramp inclined at an angle θ with the horizontal, as shown in the figure.
Part A
What is the acceleration a of the center of the hoop?
Express your answer in terms of some or all of the variables m, r, θ, and the magnitude of the acceleration due to gravity g. Recall that trigonometric functions are entered as sin(θ) and cos(θ).