(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? Consult Appendix E and the astronomical data in Appendix F

The position of a particle with mass m traveling on a helical path (see Fig. 11–48) is given by

r→ = R cos (2πz/d) î + R sin (2πz/d) ĵ + zk̂

where R and d are the radius and pitch of the helix, respectively, and z has time dependence z = v𝓏 t where v𝓏 is the (constant) component of velocity in the z direction. Determine the time-dependent angular momentum L→ of the particle about the origin.

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When solid sphere 4 m in diameter spins around its central axis at 120 RPM, it has 1,000 kg m² / s in angular momentum. Calculate the sphere's mass.

A composite disc is built from a solid disc and a concentric, thick-walled hoop, as shown below. The inner disc has mass 4 kg and radius 2 m. The outer disc (thick-walled) has mass 5 kg, inner radius 2 m, and outer radius 3 m. The two discs spin together and complete one revolution every 3 s. Calculate the system's angular momentum about its central axis.