In any situation where an object is traveling in a circular path at constant speed, the net force acting on that object points toward the center of the circle at all times.
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When you are driving a car, and you turn the steering wheel sharply to the right in order
to turn the car to the right, you "feel" as if a force is pushing your body to the
left against the door. What has actually happened is that in order for your body to follow
the car in the tight circular path, something has to push your body toward the center of
the circle-- in this case it is the driver's-side door-- and your tendency otherwise is
to travel in a straight line tangent to the circular path (Newton's first law: constant
velocity in the absence of applied force).
In any situation where an object is traveling in a circular path at constant speed, the net force acting on that object points toward the center of the circle at all times. | |
This net force is said to be centripetal ("center-seeking"), and the equation for it is a version of Newton's second law:
where ac is called centripetal acceleration. In uniform circular motion, we encounter a situation where an object traveling at constant speed is actually accelerating. In this case the acceleration is changing the direction of velocity rather than the magnitude of velocity.
Centripetal acceleration depends on speed and size of the circle: ac = v2/r where r is the radius of the circular path. Thus the greatest acceleration and greatest amount of centripetal force would be for a heavy (large mass) object going fast through a small-radius circle.
The car itself can only travel in the circle if it is acted upon by a center-seeking force. In this case, the role of that force is played by static friction between the ground and the tires. If the car is going too fast and skids off the curve, it is because there isn't enough available static friction force to steer the car (the car then follows the tangential path, or a straight line).
At the threshold speed for a skid, the centripetal force equals the maximum available static friction force:
mvmax2/r = µsmg
vmax = √(µsgr)
Note the mass independence. This, in part, explains why it is possible to post one speed limit sign for a curved highway ramp, and have the same limit apply to all kinds of vehicles.
For more examples of centripetal force, try these: