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(II) A toy gyroscope consists of a $170-\mathrm{g}$ disk with a radius of 5.5 $\mathrm{cm}$ mounted at the center of a thin axle 21 $\mathrm{cm}$ long (Fig. 41$)$ . The gyroscope spins at 45 $\mathrm{rev} / \mathrm{s} .$ One end of its axle rests on a stand and the other end precesses horizontally about the stand. (a) How long does it take the gyroscope to precess once around? (b) If all the dimensions of the gyroscope were doubled (radius = $11 \mathrm{cm},$ axle $=42 \mathrm{cm} )$ how long would it take to precess once?

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Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

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A gyroscope consists of a …

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Gyroscope A gyroscope flyw…

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A gyroscope flywheel of ra…

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An object made of two disk…

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Gyroscope. A certain gyro…

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A demonstration gyroscope …

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02:42

A Ferris wheel with radius…

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The rotor (flywheel) of a …

the period off position being is related to the reciprocal off the angular positional frequency. My days on the real question 11 0.13 c for the positional angular velocity with this capital on my girl here. So from this equation, we have capital omega to be equal to N G E r. Well, that I only got Now we can substitute this expression into this question. So we have pain. You're going through mg to buy. I owe makeup. Oh, my m g osh on Since the guy to school because of this shape, I will be going toe half times loss dines these off the guy that scoreboard alias off the disc. Now we have Osh Oh, the extra is equal to half off the land off Jackson. So this will be equal to a 0.105 meter. Make sure you write a ll. The variables in standard units to be consistent with the immigration could be consistent with all the units. So we blood this expression off over here. Andi can also write omega to be equal dough to buy. I'm St Quincy and frequency is given Toby 45 revolutions per second so doing that they get. And he now we can simplify this expression. Introvert sold. Let me do that on the next speech. So David vehicle does so this tool who were here in this two against allowed. So now we can drive to see Toby Acquittal du bist Grant F Dimes. Skirt off. The media's off the disc. Well, t r so no. Does that the loss storms also cancel out. Now we can solve the sea question. So we have frequency to before the five revolutions per second it is off the desk is your 0.55 meters. Thing is acceleration due to gravity on dhe small R is 105 and this is a little blue 0.611 seconds. It's gifts that guy included. So this is barred, eh? Now, for park being me, you have to go find the issue. If the radius I'm doubly now, we will lose the relationship. This one that we did a ved Let me put it in the box. So this is the expression that renews for part B. So therefore we can right now being Neil Bush the void. So the older 1st 0 the variables were used for party and they knew Ana first toe the time period for the new variables in five. So this will then be equal. Good bye. Squared consumed Stays the same. Ah, disc new. Oh, uh, Gene off on you. Well, what do I stand if my scare off disk boy over. Jean off it on. Many off the bones will cancel now. So these three cancel t also dance allowed. So we finally arrive at scared. Oh, the issue off. No radios off the days on dhe Also times Horatio, off the old radios for march The new leaders and this will be quito. Since the new radius the strays off the old radius for the guide assault. This will be over. One scared on DDE for the accident. This is one over two. This gives me new or would be old to be equal toe go. So this gives did new to the equal to dries off the wound. Now we can use our answer from part A and substitute you substitute this and to think a word and we get dean deal with equal Kivu five point to do two seconds

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