Circular Motion is the motion of an object in a circle that is accelerating (circular motion is always accelerating because of the changing direction). An object traveling in a circular motion is always changing direction, and normal force or gravitational force is causing it to continue in the motion. A object in a circular motion will continue in any direction it is going unless there is an outside force.

When a object moves at a constant speed, then its velocity, which is the same as the vector, is constantly changing. Since the velocity is changing, then it is accelerating. To accelerate, there must be a centripetal force, or Fc, a force that acts on a body moving in a circular path and is directed towards the center around which the body is moving. Centripetal Force always points towards the center of a circle which is equal to the normal force (most of the time.

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In the diagram below, if there was no centripetal force applied at V1 or V2, the object would continue to go in a straight line. The line it will continue on is tangent to it position on the circle.* V= V2 - V1 = V2 + (-V1) *

In the circular motion diagram, "r" represents the radius of the circle, "Ө" represents the angle measure of the circle, the distance from A to B represents the displacement or x, and "s" represents the chord of the circle. The triangles come from the circle graph.
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Fnet = ma
Ac = (v)2/r then Fnet = m(v)2/r
Fc = m(v)2/r = (m)Ac
T = time/angle
T = 2(pie)r/v



Examples



A 200kg rocket is placed on a giant scale on the equator of Earth. How long would a day be if the scale read zero?

Fg = 200kg x 10m/s = 2000
6000km = 6000000m
(Fg would be greater than Fn)

Fg-Fn = Fc
2000-0=Fc
2000 = 75kg(v)2/6000000m
(v)2 = 160000000
v = 12649

T = 2(pi)6000000/12649
T = 37699111.84/12649
T = 2980 s
T = 0.83 hours

The Cajun Cliffhanger used to be a ride at Great America where you would stand with your back to the inside wall of a vertical cylinder. As the cylinder turned faster and faster, eventually the floor beneath you would be lowered, leaving you "plastered" to the wall. The ride had a radius of 2.5m and a period of revolution of 2.0 seconds. Determine the minimum coefficient of friction needed to keep passengers from sliding down the wall when the floor is dropped away.

First, understand what is the question asking for - minimum coefficient of friction
Second, list out what we know - r =2.5m T= 2.0 s
with this information, we can find out the velocity by T= 2πr / v
2.0 s= 2 x π x 2.5m / v
v=7.85m/s
After we find the velocity, we can find Fc by Fc= mv^2 / r
Fc=m x 7.85^2 / 2.5m
Fc= 24.649m
Since mass is not given, we cannot go further from here. We need to try the other direction.
The question is looking for the friction coefficient, Friction = µ x the force perpendicular to friction.
Friction is keeping us from not falling in this case, therefore, friction is equal to Fg since vertically the person is not accelerating.
Fg= µ x the force perpendicular to friction (Fc in this case.)
9.8m= µ x Fc
From the calculation above, Fc= 24.649m 9.8m= µ x 24.649m
mass cancel out 9.8= µ x 24.649
µ = 2.5 2