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$\cdot$ The rotor (flywheel) of a toy gyroscope has a mass of 0.140 kg. Its moment of inertia about its axis is $1.20 \times$ $10^{-4} \mathrm{kg} \cdot \mathrm{m}^{2} .$ The mass of the frame is 0.0250 $\mathrm{kg} .$ The gyro- scope is supported on a single pivot (see Figure 10.68 ) with its center of mass a horizontal distance of 4.00 $\mathrm{cm}$ from the pivot. The gyroscope is precessing in a horizontal plane at the rate of 1 revolution in 2.20 s. (a) Find the upward force exerted by the pivot. (b) Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min. (c) Copy the diagram and draw vectors to show the angular momentum of the rotor and the torque acting on it.

a) 1.62 $\mathrm{N}$b) $1.8 \times 10^{3}$ rev/minc) See drawing

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

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So we know that the pre session angular velocity we're going to denote this as capital omega. So Capital omega will equal to pi over the period of the procession. Ah, and we know that this is simply going to be equal Teo to pie divided by 2.2 So we can say 2.856 radiance per second. And we know that the total mass will be equal to the mass of the Roeder, plus the mass of the frame. So this will be 0.140 plus 0.140 0.0 to 5. And we know that the mass total is going to be equal to 0.165 kilograms. So for party, when we want the force soapy weaken, take this going to be equal to the weight total and this is going to be equal to the total mass times G, or we can say 0.165 kilograms times 9.8 meters per second. And this is giving us 1.6 to Newton's and report for part B. They want us to find the angular velocity. This will be the wait Total times the radius divided by the ah by the moment of inertia times the precession angular velocity. So this will be a point 165 again times 9.8 times the radius of 0.4 meters, divided by the ah, moment of inertia. 1.2 times 10 to the negative fourth and then the precession and angular velocity, 2.856 radiance per second. And this is equaling 189 or Etienne's per second. So that's your answer for part a prancer for part B for part. See, you simply want to copy the diagram. Eso you can copy that diagram the main. The main thing here is that when you copy the diagram, the torque of the Roder is going to be is in the direction of the precession. And then when you copy the diagram, one more key factor is that the angular momentum of the rotor is along the axis of the rotor away from the pivot. So essentially, you're just copying the exact diagram you know verbatim from the textbook, and then make sure that the torque of the rotor is in the direction of of the procession. And then the angular momentum of the rotor is along the axis of the rotor again, away from the pivot. That is the end of the solution. Thank you for watching.

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