The rotor (flywheel) of a toy gyroscope has a mass of 0.150 kg. Its moment of in

Question

The rotor (flywheel) of a toy gyroscope has a mass of 0.150 kg. Its moment of inertia about its axis is 1.30 times 10^-4 kg. m^2. The mass of the frame is 0.0255 kg. The gyroscope is supported on a single pivot (see the figure below (Figure 1^) with its center of mass a horizontal distance of 4.05 cm from the pivot. The gyroscope is processing in a horizontal plane at the rate of 1 revolution in 2.30 s. Find the upward force exerted by the pivot. Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min. Draw vectors to show the angular momentum of the rotor and the torque acting. The angular momentum force vector should begin at the center of a black dot. The orientation of your vectors will be graded. Positive torque is considered to be in the counterclockwise direction. The direction of the torque can be change by clicking the dot next to tau.

Explanation / Answer

PART A)

total mass of gyroscope mtotal= 0.150 +0.0255 = 0.1755 kg

F = wtotal = 0.1755*9.8 = 1.72 N

PART B)

Angular speed = wr/(iW)= 1.72*0.0405/(1.3*10^-4*2 pi /2.3) = 196.15 rad/s

= 1.87 * 10^3 rev/min

PART C) If the figure in the problem is viewed from above, torque is in the direction of the precession and ANGULAR MOMENTUM  is along the axis of the rotor, away from the pivot.

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