PHY183-Lecture29 - Newtons Second Law for Rotation Newtons...

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1 March 15, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 29 Precession, Torque and Angular Momentum Demos and Examples Newton’s Second Law for Rotation Newton’s Second Law for Rotation: Yesterday we saw that taller trees will fall more slowly than shorter trees. The angular acceleration is proportional to 1/L Consider how easy it is to balance a long thin rod, compared to a similar short thin rod Increasing the moment of inertia of a rod having a fixed length will also make it easier to balance the rod 3/15/2012 Physics for Scientists&Engineers 1 2 τ = I α Clicker Quiz A person is seated on a stool that is free to rotate about the vertical axis (friction is negligible). The person is holding a wheel whose axis is aligned vertically and the wheel is spinning rapidly in the counterclockwise direction (as seen from above). The person rotates the wheel 180 degrees such that the wheel’s axis is aligned vertically, but it is now spinning clockwise as seen from above. The person and stool will: A. rotate clockwise as seen from above B. rotate counterclockwise as seen from above C. not rotate 3/15/2012 Physics for Scientists&Engineers 1 3 Precession The axis of a spinning top wobbles as the top slows down Precession Imagine we have a top with mass m spinning with angular frequency ω along an axis that makes an angle ϕ with the vertical The torque is given by The top will precess with a frequency 3/15/2012 Physics for Scientists&Engineers 1 4 ω p = rmg I note that p increases as decreases = d L dt sin sin L d dr m g dr m g rmg dt dt L dt I φ θθ θ = = = Precession Demos Gyroscope Pivot point below gyroscope’s center of mass – does not precess Pivot point offset from gyroscope’s center of mass The gravitational force no longer acts through the pivot and a net torque acts on the gyroscope, so its angular momentum will change: we get precession 3/15/2012 Physics for Scientists&Engineers 1 5 Clicker Question Clicker Question: If the mass distribution of the gyroscope is rearranged such that its center of mass is on the opposite side of the pivot point than it was in the previous demo, then A. The gyroscope will not precess B. The gyroscope will precess in the same direction as before C. The gyroscope will precess in the opposite direction than before 3/15/2012 Physics for Scientists&Engineers 1 6
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2 Precession Demos (2)
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PHY183-Lecture29 - Newtons Second Law for Rotation Newtons...

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