6 Apr 2015

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PHYS 17200 - Modern Mechanics - Lecture 17_Multiparticle Systems

Rotational Kinetic Energy

● Just as a vibrating object has kinetic energy associated with vibration, even if its center

of mass is at rest, so a rotating object has kinetic energy associated with rotation, even if

its center of mass is at rest

● Krotational = ½ * I * ω2

● I = m1r2 + m2r2 + m3r2 +m4r2 + … (inertia depends on the shape of an object

○ Cylinder:1/12 * ML2 + ¼ MR2

○ Disk: ½ MR2

○ Sphere: MR⅖2

● Rotational Kinetic Energy + Linear Kinetic Energy = Total Kinetic Energy

○ Components include Inertia of the object and its angular velocity

Angular velocity

● ω = 2pi/T

○ T = period = time (seconds) for one complete rotation

● v = 2pir/T = ω*r