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please explain what is uniform circular motion with examples?
Uniform Circular Motion
Uniform motion can be described as an object with constant mass that travels in a perfectly circular path with uniform, i.e. constant magnitude, velocity. To be circular, the path must have a constant distance or radius from the center of the circle, and the description of the direction of the velocity is particularly simple: its magnitude is constant and its direction is always tangential to the circular path at every position of the object.
At any instant coordinates of the material in motion can be found using x - x0 = rcosθ y - y0 = rsinθ
Where (x0 , y0) are the initial coordinates of the particle at t=0.
Velocity: The speed of travel around the orbit is v = r dθ /dt = ω r, where the angular rate of rotation is ω.
Acceleration: For a angle dθ = ω dt the change in v is a vector at right angles to v and of magnitude v dθ, which in turn means that the magnitude of the acceleration is given by a = v dθ / dt = vω = v2 / r
For any object to travel in a uniform circular path, it must be subjected to a force which
1. Is always directed centripetally, i.e. in towards the center of the circular path. 2. Has a constant magnitude equal to mv2/r.
Centripetal Force: The centripetal force is the external force required to make a body follow a curved path. Hence centripetal force is a kinematic force requirement, not a particular kind of force like gravity or electromagnetism. Any force or combination of forces can act to provide a centripetal force.
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