666662 1 - University of Wisconsin–Plattevillepeople.uwplatt.edu/~vonmaluskid/D/day26.pdfRolling...

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Transcript of 666662 1 - University of Wisconsin–Plattevillepeople.uwplatt.edu/~vonmaluskid/D/day26.pdfRolling...

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Common Moments of Inertia ∑=i

iirmI 2

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Static Equilibrium

If the net torque is 0, no rotation will occur.

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Example

A 40kg 5m long beam is supported (not attached) to the two posts in the figure. A 20kg boy starts walking along the beam. How close can he get to the right end of the beam without it falling over?

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Rank these 4 from easiest to hardest to hold without the meter stick rotating.

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Rolling Motion

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Rolling without slipping

When the wheel makes one full rotation it travels a distance equal to the circumference:

Where T is the time for one revolution.

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Note: The bottom of the wheel is instantaneously at rest. The top of the wheel is moving with twice the translational velocity.

The point of contact is the pivot point but the wheel rotates about the center.

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Demo: Tricycle

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Energy in rolling

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Example

Different shapes start at the top of a ramp and are released with zero initial velocity. Which reaches the bottom first if they have the same mass?

Demo: Do it