16. Angular Momentum

Intro to Angular Momentum

Multiple Choice
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.
Multiple Choice
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.
Open Question
(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
Open Question
(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
Open Question
CALC A hollow, thin-walled sphere of mass 12.0 kg and diameter 48.0 cm is rotating about an axle through its center. The angle (in radians) through which it turns as a function of time (in seconds) is given by θ(t) = At^2 + Bt^4, where A has numerical value 1.50 and B has numerical value 1.10. (a) What are the units of the constants A and B?
Open Question
A woman with mass 50 kg is standing on the rim of a large disk that is rotating at 0.80 rev/s about an axis through its center. The disk has mass 110 kg and radius 4.0 m. Calculate the magnitude of the total angular momentum of the woman–disk system. (Assume that you can treat the woman as a point.)
Open Question
What is the angular momentum vector of the 2.0 kg, 4.0-cm-diameter rotating disk in FIGURE EX12.43? Give your answer using unit vectors.
Open Question
What is the angular momentum vector of the 500 g rotating bar in FIGURE EX12.44? Give your answer using unit vectors.
Open Question
(I) (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?
(b) How much torque is required to stop it in 6.0 s?
Open Question
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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