Formula for centripetal force
Consider an object of mass m moving with constant angular velocity (
w) and constant speed (v) in a circle of radius r with centre O (see Figure
1).
It moves from P to Q in a time t.
Change in velocity parallel to PO = vsin
q - 0
Change in velocity perpendicular to PO = vcos
q - v
When
q becomes small (that is when
Q is very close to P) sin
q is close to
q in radians and cos
q tends to 1.
The equations then become:
Change in velocity
along PO = v
q - 0 = v
qChange in
velocity perpendicular to PO = v - v = 0
Therefore acceleration along PO = v
q/t = v
w = v
2/r =
w2r
Applying Newton's Second Law (F = ma)
gives:
