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Transcript
Dynamics of Uniform Circular Motion UCVTS AIT Physics Dynamics of Uniform Circular Motion • Uniform circular motion is the motion of an object traveling at a constant speed on a circular path • The period T is the time required for the object to travel once around the circle • The speed v of the object is related to the period and the radius of the circle by C (circumference) 2 r d 2 r v T – Example 1 and 2 UCVTS AIT Physics Dynamics of Uniform Circular Motion • Centripetal Acceleration – An object in uniform circular motion experiences an acceleration (even at constant velocity...because its direction is changing), known as centripetal acceleration. The magnitude of the centripetal acceleration is 2 v ac r – where v is the speed of the object, and r is the radius of the circle. Example 3 ac is always pointing toward the center of the circle UCVTS AIT Physics Dynamics of Uniform Circular Motion • Centripetal Force – To produce a centripetal acceleration, a net force pointing towards the center of the circle is needed…remember……F=ma....a=F/m – – where m is the mass of the object, v is the speed of the object, and r is the radius of the circle. As v increases, so will the tension in the string (Fc) UCVTS AIT Physics NOTES about Dynamics of Uniform Circular Motion UCVTS AIT Physics Dynamics of Uniform Circular Motion • • Centripetal force and Centrifugal force are the action-reaction force pair associated with circular motion. According to Newton's first law of motion, a moving body travels along a straight path with constant velocity unless it is acted on by an outside force. – For circular motion to occur there must be a constant force acting on a body, pushing it toward the center of the circular path • This force is the centripetal (“center-seeking”) force – For a planet orbiting the sun, the force is gravitational – an object twirled on a string, the force is mechanical – for an electron orbiting an atom, it is electrical • According to Newton's third law of motion, for every action there is an equal and opposite reaction. The centripetal force, the action, is balanced by a reaction force, the centrifugal (“center-fleeing”) force. The two forces are equal in magnitude and opposite in direction. The centrifugal force does not act on the body in motion; the only force acting on the body in motion is the centripetal force. • The centrifugal force is often mistakenly thought to cause a body to fly out of its circular path when it is released; rather, it is the removal of the centripetal force that allows the body to travel in a straight line as required by Newton's first law. UCVTS AIT Physics Applications of Dynamics of Uniform Circular Motion • Banked Curves FN is normal to the surface and is the force that the road applies to the car FN has a component FN sin that pushes towards the center and provides the centripetal force mv 2 FC FN sin r • The components of the normal force FN cos must balancethe weight mg therefore FN cos mg dividing this equation in to the previous FN sin mv 2 FN cos r • v2 tan rg Do example 8 UCVTS AIT Physics Vertical Circular Motion and Roller Coasters! mv 2 F r UCVTS AIT Physics