Uniform circular motion

Motion in a circle of constant radius at constant speed.Instantaneous velocity is always tangent to the circle (thus if suddenly released, object will fly tangentially and not out of the circle, because centripetal force is being applied to overcome natural tendency of object to move in a straight line)Centripetal acceleration (rate of change of velocity): Always directed towards the center of the circle.Centripetal force: The net force required to provide circular motion. In carscenario, it is the friction acting on the turned wheels of the car. In swinging bucket scenario, it is the tension in the spring. In orbital scenario, it is the force of gravity acting on the orbiting object (e.g. moon)No work done as net centripetal force is at right angle to displacement at all times about the circle.Velocity, acceleration and momentum changes (because direction is always changing). Meanwhile speed and kinetic energy remain constant.For racing track consisting of two rings (one inner and one outer): Friction force on wet day on two rings is the same. For racing car to negotiate safely at same speed around bend, outer ring will be better for car to travel because centripetal force will be less than friction force.For car turning around a bend/corner, the friction force between the tyres and the road acts towards the centre of the circular motion.Explain why the passengers feel as if they are being “thrown outwards”: Friction between passengers and the seat provides the centripetal force causing an initial turning effect on the lower part of the body. However due to inertia the upper body continues to move in a straight line, hence passengers experiencing the feeling of being “thrown outwards”.On banked curve:Without banking, there is no component of force in horizontal direction, thus on wet days friction is lowered hence dangerous. However with banking, there is a component of the normal force in direction towards centre of circle, reduced reliance on friction hence safer on wet days. (thus cyclist must lean towards the side when going round a bend)Car travelling in a circle towards the right: 3 (NR, fL, fR) forces acting on right wheel producing anticlockwise moment, only one (NL) acting on left wheel producing clockwise moment. Hence if loses contact, car would flip away from centre of circle, anticlockwise direction (taking centre of car to be centre of circle)Conical pendulum:Vertical circular motion: For object to complete circle without falling off, T>0. When T=0, object loses contact and string comes loose. At the top: and at the bottom: . Hence (in order not to lose contact at the top)Car going over a hump: . Car leaves surface when R/N = 0Airplane turning: Resultant of Lift vector and Weight vector gives centripetal force (use sine or cosine rule to find derive magnitude of forces from w=mg)For Satellite in circular orbit:!!!!!!Explain why, although the satellite is moving at constant speed, it is not in equilibrium: The direction of the satellite is always changing, undergoing acceleration, indicating the action of a resultant force on the satellite, which is the gravitational pull of the planet. Projectile motion: When a body is projected into the air at an angle to the vertical and moves in a parabolic path (in the absence of air resistance).KNOW HOW TO DRAW DIRECTIONS OF HORIZONTAL AND VERTICAL VELOCITIES ALONG PATH OF MOTION:Vx maintained at same length.Vy gets shorter reaching the top, then longer as the object falls towards the earth.Maximum height, time taken and range travelled are NOT affected by mass of ballistic.Maximum height, time taken and range are affected by angle of launch and magnitude of vertical/horizontal velocity. . Hence, smaller angle, lower maximum height, longer range travelled.Presence of wind blowing at constant horizontal speed in direction of projectile: Maximum height UNAFFECTED, range travelled INCREASES.

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