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Physics 103: Lecture 12 Rotational Kinematics
Today’s lecture will cover rotational kinematics centripetal force March 2004 Physics Spring 1
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Rotation s q = Dq Dw s w = a = Dt Dt q R R March 2004
Revolutions, radians, degrees March 2004 Physics Spring
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Vector Nature of Angular Quantities
Right hand rule Grasp the axis of rotation with your right hand Wrap your fingers in the direction of rotation Your thumb points in the direction of w March 2004 Physics Spring
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Centripetal Acceleration
V2 Force is required to change motion i.e. velocity (magnitude and direction) V1 magnitude is constant, but direction changes DV points toward the center of rotation V1 V2 DV Centrifugal force? March 2004 Physics Spring
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Centripetal Acceleration
March 2004 Physics Spring
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Rotation Summary (with comparison to 1-D kinematics)
Angular Linear And for a point at a distance R from the rotation axis: x = Rv = R a = R March 2004 Physics Spring
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Total Acceleration The tangential component of the acceleration is due to changing speed The centripetal component of the acceleration is due to changing direction Total acceleration can be found from these components March 2004 Physics Spring
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Lecture 13, Preflight 1 & 2 You and a friend are playing on the merry-go-round at Carle Park. You stand at the outer edge of the merry-go-round and your friend stands halfway between the outer edge and the center. Assume the rotation rate of the merry-go-round is constant. Who has the greatest angular velocity? 1. You do 2. Your friend does 3. Same CORRECT You both cover the same angle in the same amount of time. March 2004 Physics Spring
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Lecture 13, Preflight 3 & 4 Who has the greatest tangential velocity?
1. You do 2. Your friend does 3. Same CORRECT for a given angular speed, the tangential speed is directly proportional to the radius Demos: Use 1) turntable with stoppers (friction and centripetal acceleration) 2) Bucket with water 3) Ball with string and knife to cut. March 2004 Physics Spring
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Lecture 13, Preflight 5 & 6 Who has the greatest centripetal acceleration? 1. You do 2. Your friend does 3. Same CORRECT centripetal acceleration = rw2 - you have a larger radius so therefore you have a larger centripetal acceleration March 2004 Physics Spring
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Your Car Your Friends Car March 2004 Physics Spring
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Lecture 13, Preflight 7 & 8 Tired of playing in the park, you and your friend hop into your cars and decide to drive over to Michael’s Frozen Custard. During some part of your trip down Monroe Street your cars are side by side and have the same speed and the same acceleration. The wheels on your 1965 Corvette Stingray have a larger radius than the wheels on your friends 1986 Chevette Hatchback. Which car's wheels have the greatest angular acceleration? 1. Corvette 2. Chevette 3. Same CORRECT The Chevette's wheels have a smaller circumference than the Corvette's wheels therefore the wheels of the Chevette must make more rotations to keep up. March 2004 Physics Spring
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Forces Causing Centripetal Acceleration
Newton’s Second Law says that the centripetal acceleration is accompanied by a force F = maC F stands for any force that keeps an object following a circular path Tension in a string Gravity Force of friction March 2004 Physics Spring
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Problem Solving Strategy
Draw a free body diagram, showing and labeling all the forces acting on the object(s) Choose a coordinate system that has one axis perpendicular to the circular path and the other axis tangent to the circular path Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration) Solve as in Newton’s second law problems The directions will be radial and tangential The acceleration will be the centripetal acceleration March 2004 Physics Spring
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Applications of Forces Causing Centripetal Acceleration
Many specific situations will use forces that cause centripetal acceleration Level curves Banked curves Horizontal circles Vertical circles March 2004 Physics Spring
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Level Curves Friction is the force that produces the centripetal acceleration Can find the frictional force, µ, v March 2004 Physics Spring
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Banked Curves A component of the normal force adds to the frictional force to allow higher speeds Can the ability of car to turn be made independent of the coefficient of friction? Yes No March 2004 Physics Spring
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Example An automobile successfully turns on a very icy roadway (no friction). This means that the net external force is just what is needed to provide the centripetal acceleration. g tan q = V2 R Note that there is no dependence on m, (which is good since it is zero!! ) March 2004 Physics Spring
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Horizontal Circle The horizontal component of the tension causes the centripetal acceleration March 2004 Physics Spring
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Vertical Circle Look at the forces at the top of the circle
The minimum speed at the top of the circle can be found Should we be worried about the mass of the people on the roller coaster? Yes No March 2004 Physics Spring
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Rotation Summary (with comparison to 1-D kinematics)
Angular Linear And for a point at a distance R from the rotation axis: x = Rv = R a = R March 2004 Physics Spring
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