PHYS 17200 Lecture 17: Multiparticle Systems

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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: MR2
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
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