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Transcript
Circular Motion AP Physics 1 Uniform Circular Motion Uniform Circular Motion Uniform circular motion describes an object that travels along a circular trajectory at a constant speed. The velocity of the object is always tangent to the trajectory of the object. The magnitude of the velocity for uniform circular motion is defined using the circumference of the path and the period. Period (T) is the amount of time required to travel once around the circle. Centripetal Acceleration Although the speed of the object is constant, the velocity is not; it is always changing direction. Because the velocity is changing, the object is accelerating! The acceleration for uniform circular motion points towards the center of the circle, it is referred to as centripetal acceleration. Forces and Circular Motion Centripetal Force A particle of mass m moving at constant speed v around a circle of radius r must always have a net force of magnitude mv2/r pointing toward the center of the circle. This is not a new kind of force: The net force is due to one or more of our familiar forces such as tension, friction, or the normal force. Centripetal force does not go on an FBD! Example An ice hockey puck is tied by a string to a stake in the ice. The puck is then swung in a circle. What force is producing the centripetal acceleration of the puck? Example A coin sits on a turntable as the table steadily rotates counterclockwise. What force or forces act in the plane of the turntable? Example What is the maximum speed with which a 1500 kg car can make a turn around a curve of radius 20 m on a level (unbanked) road without sliding? Assume the coefficient of static friction is 1.0. Centrifugal Force If you are a passenger in a car that turns a corner quickly, it is the force of the car door, pushing inward toward the center of the curve, that causes you to turn the corner. What you feel is your body trying to move ahead in a straight line as outside forces (the door) act to turn you in a circle. A centrifugal force will never appear on a freebody diagram and never be included in Newton’s laws. Because its not real. At all. Non-Uniform Circular Motion: Vertical Circles Non-Uniform Circular Motion If an object moves in a vertical circle, the motion is not uniform (speed is not constant). In this course, we will only analyze motion at the top and bottom of a vertical loop. We can use this to analyze the “weirdness” experienced while moving through a roller coaster loop. As you move through a vertical loop, you feel strange effects at the top and the bottom. Apparent weight (how heavy you feel) is the normal force provided by the track. The normal force is larger at the bottom than the top, which is why you feel heavier at the bottom of the track. Critical Speed For an object moving in a vertical circle, there is a minimum speed it must have to not fall off the track. This minimum speed occurs when the normal force is equal to 0. If the normal force equals 0, the cart is no longer in contact with the track. 𝑚𝑣 2 𝑚𝑣 2 𝐹𝑐 = → 𝑁 + 𝑚𝑔 = 𝑟 𝑟 𝑁=0 𝑚𝑣 2 𝑚𝑔 = → 𝑣𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = 𝑟𝑔 𝑟 Example A physics textbook swings back and forth as a pendulum. Which is the correct free-body diagram when the book is at the bottom and moving to the right? Example A person drives over a circular hill. Determine whether the force of gravity or the normal force on the car is larger. The Gravitron The Gravitron is a fun application of circular motion. This carnival ride spins fast enough that the riders appear to defy gravity. As the ride speeds up, the normal force on the rider increases, which in turn increases the force of friction acting on the rider. If this frictional force is large enough, it will perfectly cancel out the force of gravity!