A tire 0.700 m in radius rotates at a constant rate of 180
rev/min. Find the speed and acceleration of a small stone lodged in
the tread of the tire (on its outer edge).
B- What is the acceleration of the stone?
is it toward the center of the path?
OR tangent to the path ?
OR away from the center of the path?
First you want to find the angular velocity which requires some
(180 rev/min)(1 min/60 sec)(2 pi radians/1 rev) = 6pi = 18.84
Linear velocity is related to angular velocity by v =
v = (18.84 rad/s)(.7) = 13.188
a = v^2/R = (13.188)^2 /(.7) = 248.46192 m/s^2
It will point towards the center of the path