5.1- Uniform Circular Motion
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Uniform circular motion is the motion of an object traveling at a constant speed on a circular path.
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The
period T is the amount of time required to travel once around the circle, that is, to make one complete revolution.
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Centripetal acceleration occurs when the acceleration points towards the center.
5.2- Centripetal Acceleration
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When an object is released from a path of circular motion, it continues to move in a straight line.
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During centripetal acceleration, the object is constantly accelerating towards the center.
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The smaller the radius of the circular path is, the smaller the centripetal acceleration.
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An object in uniform circular motion can never be at equilibrium.
5.3- Centripetal Force
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The net force causing centripetal acceleration is called
centripetal force.
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The centripetal force points in the same direction as the centripetal acceleration- towards the center.
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The smaller the circular arc is, the smaller the centripetal force required to produce the centripetal acceleration must be.
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Greater speeds and tighter turns require greater centripetal forces.
5.4- Banked Curves
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The angle at which a friction-free curve is banked depends on the radius of the curve and the speed at which the curve is to be negotiated.
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Greater speeds and smaller radii require more steeply banked curves, or larger angles.
5.5- Satellites In Circular Orbits
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Satellites in circular orbits, have uniform circular motion.
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These satellites are kept on path by a centripetal force provided by the gravitational pull of the Earth.
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The closer the satellite is to Earth, the smaller the radius of the orbit will be. The orbital speed must be greater as well.
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When determining orbital speed, mass does not matter.
5.6- Apparent Weightlessness & Artificial Gravity
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The condition of apparent weightlessness is similar to what occurs in an elevator during its free-fall.
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Objects in uniform circular motion constantly accelerate, or "fall" towards the center of the circle, in order to remain on the circular path.
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The apparent weight in a satellite is zero.
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The surface of the rotating object pushes on any objects it contacts, and thereby provides the centripetal force that keeps the object moving on a circular path.
5.7- Vertical Circular Motion
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At each point on a vertical circle, the centripetal force is the net sum of all the force components oriented along the radial direction and pointed toward the center of the circle.
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At the bottom of a vertical circle, the normal force and the weight oppose one another.
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At the top, the normal force and weight reinforce one another.
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At points 2 and four on the sides, the weight is tangent to the circle and has no component pointing towards the center.