 #1
wcjy
 73
 10
 Homework Statement:

A small sphere of radius r_0 = 1.5 cm rolls without slipping on the track which is fixed on the
ground as shown in Figure 3(a). The radius of the track is R_0 = 26 cm. The sphere is released
from rest at height R_0 above the bottom of the track and rolls without slipping down the track.
(a) What is the angular velocity of the sphere when it leaves the track after passing through
an angle 125° as shown in Figure 3(a)
(b) What is the net acceleration of the sphere the moment before it leaves the track?
(c) At what distance D from the base of the track will the sphere hit the ground?
 Relevant Equations:

Conservation of Energy
a_c = v^2 / r
(a) Using COE,
$$mgh = 0.5mv^2 + 0.5I\omega^2$$
I solved it, where $$\omega = 112 rad/s$$
(b) This is the part where I have question or problem.
I saw my course mate working and he start of with finding centripetal acceleration.
$$a_c = \frac{v^2}{r} = \frac{(r_0\omega)^2}{R_0}$$
Why isn't it:
$$a_c = R_0\omega^2$$