RigidBody

# RigidBody - Mechanics and Modern Physics Dr. Bernd Stelzer...

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Dr. Bernd Stelzer Mechanics and Modern Physics PHYS 120 SFU Fall 2010 Dr. Bernd Stelzer

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Rotation of a Rigid Body November 3, 2010 Not all motion can be described as that of a particle . Rotation requires the idea of an extended object. This diver is moving toward the water along a parabolic trajectory, yet, she’s rotating rapidly around her center of mass. Chapter Goal: To understand the physics of rotating objects. PHYS120 2
Rotational Energy November 3, 2010 • A rotating rigid body has kinetic energy (all atoms are in motion!) • An objects rotational kinetic energy is the sum of the kinetic energies of all of the moving particles. K rot = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 + ... = 1 2 m i v i 2 i = 1 2 m i r i 2 i ω 2 = 1 2 2 m i r i 2 i PHYS120 3 K i = 1 2 m i v i 2 K rot = 1 2 I 2 Moment of Inertia v = r

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Rotational Energy November 3, 2010 K rot = 1 2 I ω 2 • An object’s moment of inertia depends on the axis of rotation and mass distribution around it. • Objects with larger moment of inertia are harder to rotate. = r 2 dm I = m i r i 2 i PHYS120 4 Moment of Inertia: Rotational Kinetic Energy: SI Units: [kg m 2 ] Particles Continuous Object
Rotating System of Particles November 3, 2010 PHYS120 5 An object consists of four point particles, each of mass m , connected by rigid massless rods to form a rectangle with edge lengths 2a and 2b . The system rotates with angular speed ω about an axis in the plane of the rectangle and through its center. (a) Find the kinetic energy of the object. (b) Check your result by calculating the kinetic energy of each particle and adding them. v t = ω r = a

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Rotating System of Particles November 3, 2010 PHYS120 6 The same object now rotates with the angular speed ω about an axis in the plane of the rectangle and through particles 1 and 3. a) Find the kinetic energy of the object. Displacing the rotation axis changes the moment of inertia and the kinetic energy.
Moments of Inertia (Continuous Objects) November 3, 2010 PHYS120 7 Calculate the moment of inertia I of a thin rod of mass M and length L about an axis perpendicular to the rod and through one end. = 1 3 ML 2

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Moments of Inertia (Continuous Objects) November 3, 2010 PHYS120 8 Thin Hoop Disc = MR 2 = MR 2
Moments of Inertia (Continuous Objects) November 3, 2010 PHYS120 9 Solid Cylinder

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Moments of Inertia November 3, 2010 PHYS120 10
Dr. Bernd Stelzer Mechanics and Modern Physics PHYS 120 SFU Fall 2010 Dr. Bernd Stelzer

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