PHY183-Lecture26 - Rotation We have been treating bodies by...

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1 March 12, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 27 Rotation March 12, 2012 Physics for Scientists&Engineers 1 2 Rotation We have been treating bodies by looking at the motion of the center of mass We introduced the concept of motion of the center of mass + rotation about the center of mass We have covered circular motion of the center of mass Now we will study rotation We will concentrate on the rotation of solid, extended objects March 12, 2012 Physics for Scientists&Engineers 1 3 Rotation of Non-Solid Extended Objects Andromeda Galaxy Hurricane March 12, 2012 Physics for Scientists&Engineers 1 4 Kinematics of Circular Motion We start with some familiar concepts that we introduced to describe circular motion Angular position Angular velocity Angular acceleration ω = d θ dt α = d dt = d 2 dt 2 March 12, 2012 Physics for Scientists&Engineers 1 5 Linear and Circular Motion We related the variables describing circular motion to the variables describing linear motion Displacement, velocity, and acceleration Kinetic energy for linear motion Kinetic energy for rotation (point particle) s = r v = r a t = r a c = 2 r a = a c 2 + a t 2 K = 1 2 mv 2 K = 1 2 mv 2 = 1 2 m ( r ) 2 = 1 2 mr 2 2 March 12, 2012 Physics for Scientists&Engineers 1 6 Several Point Particles Now let’s discuss the kinetic energy of several point particles K = K i i = 1 n = 1 2 m i v i 2 i = 1 n = 1 2 m i i = 1 n r i 2 i 2
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2 March 12, 2012 Physics for Scientists&Engineers 1 7 Several Point Particles If we assume that these particles keep their distances fixed with respect to each other (solid object, all moving with the same angular velocity) we can write Where I is the moment of inertia given by In Chapter 9, we saw that all quantities associated with circular motion have equivalents in linear motion K = 1 2 m i i = 1 n r i 2 ω 2 = 1 2 m i i = 1 n r i 2 2 = 1 2 I 2 I = m i i = 1 n r i 2 Compare K linear = 1 2 mv 2 K circular = 1 2 I 2 Clicker Quiz Consider two masses each of mass m They are connected by a thin, massless rod In the three drawings below, the two masses spin in a horizontal plane around a vertical axis represented by dashed line Which of the systems has the highest rotational inertia? March 12, 2012 Physics for Scientists&Engineers 1 8 Clicker Quiz Solution March 12, 2012 Physics for Scientists&Engineers 1 9 I = m r 2 2 + m r 2 2 I = 1 2 mr 2 I = m r 5 2 + m 4 r 5 2 I = 17 25 mr 2 I = m 0 () 2 + mr 2 I = mr 2 March 12, 2012 Physics for Scientists&Engineers 1 10 Moment of Inertia Demos Mass is the property of objects that resists changes in linear motion Moment of inertia is the property of an extended object that resists changes in rotation Two bars One red bar One blue bar • Wiggle the bars back and forth Two rotating masses
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This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture26 - Rotation We have been treating bodies by...

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