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Transcript
Circular Motion Centripetal Force Key Question: Why does a roller coaster stay on a track upside down on a loop? Centripetal Force • We usually think of acceleration as a change in speed. • Because velocity includes both speed and direction, acceleration can also be a change in the direction of motion. Centripetal Force • Any force that causes an object to move in a circle is called a centripetal force. • A centripetal force is always perpendicular to an object’s motion, toward the center of the circle. Centripetal Force Mass (kg) Centripetal force (N) Fc = mv2 r Linear speed (m/sec) Radius of path (m) Calculate centripetal force • A 50-kilogram passenger on an amusement park ride stands with his back against the wall of a cylindrical room with radius of 3 m. • What is the centripetal force of the wall pressing into his back when the room spins and he is moving at 6 m/sec? Centripetal Acceleration • Acceleration is the rate at which an object’s velocity changes as the result of a force. • Centripetal acceleration is the acceleration of an object moving in a circle due to the centripetal force. Centripetal Acceleration Centripetal acceleration (m/sec2) ac = v2 r Speed (m/sec) Radius of path (m) Calculate centripetal acceleration • A motorcycle drives around a bend with a 50-meter radius at 10 m/sec. • Find the motor cycle’s centripetal acceleration and compare it with g, the acceleration of gravity. Centrifugal Force We call an object’s tendency to resist a change in its motion its inertia. An object moving in a circle is constantly changing its direction of motion. • Although the centripetal force pushes you toward the center of the circular path... • ...it seems as if there also is a force pushing you to the outside. This apparent outward force is called centrifugal force. Centrifugal Force Centrifugal force is not a true force exerted on your body. It is simply your tendency to move in a straight line due to inertia. • This is easy to observe by twirling a small object at the end of a string. • When the string is released, the object flies off in a straight line tangent to the circle. Torque • The door is free to rotate about an axis through O • There are three factors that determine the effectiveness of the force in opening the door: • The magnitude of the force • The position of the application of the force • The angle at which the force is applied Torque, cont • Torque, t, is the tendency of a force to rotate an object about some axis • t=rF • t is the torque • F is the force • symbol is the Greek tau • r is the length of the position vector • SI unit is N.m Direction of Torque • Torque is a vector quantity • The direction is perpendicular to the plane determined by the position vector and the force • If the turning tendency of the force is counterclockwise, the torque will be positive • If the turning tendency is clockwise, the torque will be negative Multiple Torques • When two or more torques are acting on an object, the torques are added • As vectors • If the net torque is zero, the object’s rate of rotation doesn’t change General Definition of Torque • The applied force is not always perpendicular to the position vector • The component of the force perpendicular to the object will cause it to rotate General Definition of Torque, cont • When the force is parallel to the position vector, no rotation occurs • When the force is at some angle, the perpendicular component causes the rotation General Definition of Torque, final • Taking the angle into account leads to a more general definition of torque: • t = r F sin q • F is the force • r is the position vector • q is the angle between the force and the position vector Lever Arm • The lever arm, d, is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force • d = r sin q Right Hand Rule • Point the fingers in the direction of the position vector • Curl the fingers toward the force vector • The thumb points in the direction of the torque Force vs. Torque • Forces cause accelerations • Torques cause angular accelerations • Force and torque are related