BackA toy gyroscope consists of a 170-g disk with a radius of 5.5 cm mounted at the center of a thin axle 21 cm long (Fig. 11–42). The gyroscope spins at 45 rev/s. One end of its axle rests on a stand and the other end precesses horizontally about the stand. How long does it take the gyroscope to precess once around?
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.
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.
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
(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
A hollow, thin-walled sphere of mass and diameter 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 , where A has numerical value and B has numerical value . What are the units of the constants A and B?
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.)
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.
What is the angular momentum vector of the 500 g rotating bar in FIGURE EX12.44? Give your answer using unit vectors.
A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the top's precession frequency in rpm?
(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?
The position of a particle with mass m traveling on a helical path (see Fig. 11–48) is given by = 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 = v𝓏t where v𝓏 is the (constant) component of velocity in the z direction. Determine the time-dependent angular momentum of the particle about the origin.
A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity ω, then the end of the axle is placed on a support that allows the gyroscope to precess. A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?
Consider an electron in the shell. For the electron in part (c), what is the ratio of its spin angular momentum in the -direction to its orbital angular momentum in the -direction? Note: Part (c) asked for the largest orbital angular momentum this electron could have in any chosen direction.