Centripetal Acceleration Formula
The centripetal ('center-seeking') acceleration is the motion inwards towards the center of a circle. The acceleration is equal to the square of the velocity, divided by the radius of the circular path.
ac = v2/r
ac = acceleration, centripetal, m/s2
v = velocity, m/s
r = radius, m
Centripetal Acceleration Formula Questions:
1) You are whirling a ball attached to a string such that you describe a circle of radius 75 cm, at a velocity of 1.50 m/s. What is the acceleration of the ball?
Answer: The radius, r = 75 cm = 0.75 m; the velocity, v = 1.50 m/s
ac = v2/r
ac = (1.50 m/s)2 / 0.75 m
ac = 3 m/s2
2) What is the acceleration of a motor-bike rider, if his velocity is 25 m/s on a circular track with a radius of 125 m?
Answer: The radius, r = 125 m and the velocity, v = 25 m/s.
ac = v2/r
ac = (25 m/s)2 / 125 m
ac = 5 m/s2