You can create a simple gyroscope by hanging a wheel on a string as shown in the picture. We can approximate a wheel as follows: The rim has a total mass of density of λrim = 6 kg/m and is at radius R0 = 0.25 m. We can simplify the spokes and say that there are 18 spokes that are straight lines, that go directly from the center to the rim with linear mass density λspoke = 0.2 kg/m. (a) Calculate the moment of inertia, I of the wheel. (b) We put the wheel on an axle that is 0.5 m and you give the wheel a spin of 500 rev/min. What is the precessional rate of the wheel in radians/s?

You can create a simple gyroscope by hanging a wheel on a string as shown in the picture. We can approximate a wheel as follows: The rim has a total mass of density of λrim = 6 kg/m and is at radius R0 = 0.25 m. We can simplify the spokes and say that there are 18 spokes that are straight lines, that go directly from the center to the rim with linear mass density λspoke = 0.2 kg/m. (a) Calculate the moment of inertia, I of the wheel. (b) We put the wheel on an axle that is 0.5 m and you give the wheel a spin of 500 rev/min. What is the precessional rate of the wheel in radians/s?

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Question

You can create a simple gyroscope by hanging a wheel on a string as shown in the picture. We can approximate a wheel as follows: The rim has a total mass of density of λ_rim = 6 kg/m and is at radius R₀ = 0.25 m. We can simplify the spokes and say that there are 18 spokes that are straight lines, that go directly from the center to the rim with linear mass density λ_spoke = 0.2 kg/m.

(a) Calculate the moment of inertia, I of the wheel.

(b) We put the wheel on an axle that is 0.5 m and you give the wheel a spin of 500 rev/min. What is the precessional rate of the wheel in radians/s?

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