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

Question

The rotor (flywheel) of a toy gyroscope has a mass of 0.150kg . Its moment of inertia about its axis is 1.30*10^-4 kg*m2 . The mass of the frame is 2.55*10^-2kg . The gyroscope is supported on a single pivot (see the figure below (Figure 1) ) with its center of mass a horizontal distance of 4.05cm from the pivot. The gyroscope is precessing in a horizontal plane at the rate of 1.15 revolution in 2.30s .

Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min.

Explanation / Answer

given,

mass of the toy gyroscope= 0.150 kg

moment of inertia I = 1.30*10^-4 kg m2

mass of frame = 2.55*10^-2 kg

centre of mass = 4.05 cm

no.of revolutions = 1.15

time = 2.30 sec

To find :- angular speed

L= I*O ........... (1)                   where O is omega

we have to change O from rev/sec to rad/sec

therefore O= (2*3.14)/2.30 = 2.73 rad/sec............... (2)

as given above we know I = 1.30*10^-4 kg m2

substituing (2) and (3) in (1)..., we get

L =I*O

    = (1.30*10^-4)*(2.73)

    = 3.5490* 10^-4 rev/sec

since the answer must be in rev/min, the obtained answer must be divided with 60

so   ,    L = (3.5490*10^-4) / 60 = 0.0592 * 10^-4 rev/min.

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