Answer
(a) $0.29m/s^2$, downward (b) $0.29m/s^2$, upward
Work Step by Step
To find the angular speed, use the formula $$\omega=\frac{\Delta \theta}{\Delta t}$$ Substituting known values of $\Delta \theta=1.0rev(2\pi rad/1rev.)=2\pi rad.$ and $\Delta t=36s$ yields an angular speed of $$\omega=\frac{2\pi rad.}{36s}=0.17rad/s$$ (a) Centripetal acceleration always points to the center of the circle and has a magnitude of $$a=r\omega^2$$ Substituting known values of $r=9.5m$ and $\omega=0.17rad/s$ yields an acceleration of $$a=(9.5m)(0.17rad/s)^2=0.29m/s^2$$ Since the acceleration points towards the center of the circle, the acceleration points downward. (b) Since the radius and angular speed remain the same, the magnitude of the acceleration remains the same. However, the direction of acceleration is towards the center of the circle, which is upward.
