Moment of Inertia.

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Presentation transcript:

Moment of Inertia

A rigid body is an extended object whose size and shape do not change as the object moves.

Rigid body motion is described 3 ways…. Translation: movement without rotation. Rotation: movement around a fixed point (axis) and every point on the object moves in a circle. (all points have same ώ but could have different vt if different distance from center) Combination: movement linear while rotation.

Example 1: A skater holds her arms outstretched as she spins at 180rpm. What is the angular speed of her hands if they are 140cm apart?

Example 2: A high speed drill reaches a speed of 2000rpm in 0.50sec. What is the drills angular acceleration? Through how many revolutions does it turn in this first half of a second?

Example 3: A ceiling fan with a 80cm diameter is turning 60rpm. Suppose the fan coasts to a stop 25 sec after being switched off. What is the speed of the fan blade tip after 10 seconds after switch off? Through how many revolutions does the fan turn while stopping?

An unconstrained object will rotate about its center of mass An unconstrained object will rotate about its center of mass. (diver flipping) If an object is symmetrical in size, mass and density, it is safe to assume that the center of the object IS the center of mass

F=T=ma=mrώ2 In order for a mass to rotate around its CM, it must experience centripetal acceleration and therefore force or torque.

Rotational kinetic energy (energy of motion) is created by all of the atoms in an object moving at the same time in a circular path. Remember: KE=(1/2) mv2 = (1/2)mr2ώ2

If the object rotating is a geometric shape (rod, slab, hoop, sphere) we need to adjust the KE formula to include the objects moment of inertia based on shape. Moment of inertia is equal to mr2 so … KE= (1/2) I ώ2 Moment of inertia is the rotational equivalence of mass linear.