Lecture 8 Circular Motion vector description Polar coordinate system Position Coordinates Component of angular velocity Unit vectors Velocity Relation to Cartesian Coordinates Component of Angular acceleration Acceleration Newton s Second Law Circular motion r 0 k Concept Question Circular motion and force A pendulum bob swings down and is moving fast at the lowest point in its swing T is the tension in the string W is the gravitational force exerted on the pendulum bob Which free body diagram below best represents the forces exerted on the pendulum bob at the lowest point The lengths of the arrows represent the relative magnitude of the forces Strategy Applying Newton s Second Law for Circular Motion Always has a component of acceleration pointing radially inward May or may not have tangential component of acceleration Draw free body diagram for all forces mv r is not a force but mass times acceleration and does not appear on the force diagram Choose a sign convention for radial tangential direction and check that signs for forces and acceleration are consistent Worked Example Rotating bucket A pail of mass m is full of water of mass m A string is attached to the handle of the pail which is then whirled around a vertical circle at constant speed v You may assume that the center of mass of the bucket and the water undergoes circular motion with radius R What is the minimum speed that the pail must have at the top of its circular motion if the water is not to spill out of the upside down pail For faster speeds nd the tension in the string and the magnitude of the contact force between the water and the bucket Group Problem Experiment 1 circular motion A small ball of mass m is attached to one end of a spring with spring constant k and unstretched length r The other end of the spring is attached to the central axis of a motor The motor rotates at a constant angular speed of magnitude The ball and spring rotate in a horizontal plane You may neglect the gravitational force exerted on the ball What is the radius of the orbit
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