16. Angular Momentum

The Earth has mass 5.97 × 10²⁴ kg, radius 6.37 × 10⁶ m. The Earth-Sun distance is 1.5 × 10¹¹ m. Calculate its angular momentum as it spins around itself. Treat the Earth as a solid sphere of uniform mass distribution. 

BONUS 1:Treating the Earth as a point mass, calculate its angular momentum as it spins around the Sun. 

BONUS 2:Does the Earth have linear momentum as it spins around (i) itself; (ii) the Sun?

A system is made of two small, 3 kg masses attached to the ends of a 5 kg, 4 m long, thin rod. The system rotates with 180 RPM about an axis perpendicular to the rod and through one of its ends, as shown. Calculate the system's angular momentum about its axis.

(II) A particle is at the position (x, y, z) = (1.0, 2.0, 3.0)m. It is traveling with a vector velocity (-5.0 ,+ 2.8, -3.1)m/s . Its mass is 4.3 kg. What is its vector angular momentum about the origin?

(I) Calculate the angular momentum of a particle of mass m moving with constant velocity υ for two cases (see Fig. 11–34):

(a) about origin O.

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(I) Calculate the angular momentum of a particle of mass m moving with constant velocity υ for two cases (see Fig. 11–34):

(b) about O′.

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What are the x, y, and z components of the angular momentum about the origin for a particle located at r→ = xî + yĵ + zk̂ which has momentum p→ = pₓî + pᵧĵ + p𝓏k̂?