Lecture 24: Rolling Motion - Gyroscopes - VERY NON-INTUITIVE
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1. Pure Roll of Hollow and Solid Cylinders:
In pure roll, the object is not skidding or slipping, and the speed of the center of mass equals the circumferential speed. Professor Lewin derived an equation for the acceleration of an object rolling down a ramp (under pure roll conditions). For solid cylinders with uniform mass density, this acceleration is independent of the mass and radius of these cylinders (this is rather non-intuitive). However, the acceleration is higher for a solid cylinder than it is for a hollow cylinder. This is demonstrated.
2. Applying Torque to a Spinning Wheel:
When you apply a torque to a fast spinning wheel, it moves the spin angular momentum in the direction of the torque (torque is a vector). This is called precession. This very non-intuitive concept is demonstrated with a bicycle wheel.
3. Precession of a Flywheel:
The bizarre behavior of a spinning flywheel that experiences a torque due to gravity is explored. Professor Lewin demonstrates this by suspending the axle of a fast rotating bicycle wheel from a rope. By increasing the torque, the precession frequency increases. The direction of precession can be reversed if the direction of rotation of the bicycle wheel is reversed. You can also observe this very non-intuitive behavior with a toy gyroscope.
4. Mysterious Suitcase:
A suitcase is brought in that requires special handling. There is a fast rotating flywheel inside! A student volunteers to carry the suitcase around. The suitcase behaves in a weird manner as the student turns around.
5. Gyroscope in Gimbals:
A spinning object, e.g. a coin on edge, is more stable against falling over than when it isn't spinning. This concept is used in mechanical inertial guidance systems, where a spinning wheel is mounted in gimbals to prevent torques to the axis of the wheel. Professor Lewin walks through the lecture hall with such a 3-axis gimballed gyroscope. The direction of the axis of rotation of the spinning flywheel does not change as he moves around.
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