Question

A (solid) spherical top of mass and radius is spinning with angular velocity

Answer 1

Answer:

A (solid) spherical top of mass m = 1 kg and radius R = 3 cm is spinning with angular velocity ω = 1000 rad/s at an angle θ = 60◦ from vertical. The center of the sphere is a distance ` = 6 cm along the spin axis from where the top touches the ground. All the mass of the top is in the sphere. See Figure 18, right.

(i) What is the angular momentum of the top? Express your answer in terms of m, R, and ω. Then substitute numbers: you should get L = .36 Nms.

(ii) Taking the point where the top touches the ground a pivot, what is the torque on the top from gravity? Express your answer in terms of m, `, g, and θ. Then substitute numbers: you should get τ = .509 Nm.

(iii) What is the precession rate Ω of the the top? Express your answer in terms of `, g R, and ω. Then substitute numbers: you should get Ω = 1.63 rad/s