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Legend

ac

= centripetal acceleration

v

= velocity
r = radius
Fc = centripetal force
m = mass
FN = normal force
Ff = force of friction
level.jpg (19832 bytes)
The car experiences centripetal acceleration and at the same time is kept in place without sliding by friction.

Level Curves

When we release an object swung in a circular path, it takes a net force (the resultant of all forces) acting inward that keeps the object spinning in a circle; if you let go, the net force is no longer inward, so the object flies outward.

For example, If a car travelling around a level curve.  Where does the net force acting toward the center of the curve come from?  Static friction.  So Newton's 2nd law for this situation is determined as follows:

F = ma

and, static friction, assuming car is not skidding

Ff = ms.gif (149 bytes)FN = mg

Centripetal acceleration:

ac = v2/r

In this situation,

Ff = F
mg = ma = mac = mv2/r

Therefore:

g = v2/r

As a result, we see that the greater the of the road is, the faster a car can travel without skidding.  And the car can travel in a small radius of a curve without skidding.

Car travelling around a curved road

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Circular Motion

Banked Curves

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created by Will Kuo and Stan Watterson
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