(8) If you know L‚Ĥ = 0 0 what can you say about the total angular momentum of the system?
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- Determine the angular momentum of the Earth (a) aboutits rotation axis (assume the Earth is a uniform sphere),and (b) in its orbit around the Sun (treat the Earth as aparticle orbiting the Sun).(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? (b) Calculate the magnitude of the angular momentum of the earth due to its rotation around an axis through the north and south poles, modeling it as a uniform sphere.16-57. At the instant shown the boomerang has an angular velocity w = 4 rad/s, and its mass center G has a velocity vG = 6 in./s. Determine the velocity of point B at this instant. vG = 6 in. /s 30° w = 4 rad/s 1.5 in.45 5 in.
- 3)A bug of mass m_bug = 0.20 kg is sitting on your favorite record when youdecide to turn on the record player. Your record is a solid disk of radius R = 15cm and mass m disk = 0.70 kg. Your system revs up to a constant angularspeed 2 revolutions per second. The bug is initially sitting at a distance R/2 = 7.5cm, but being a thrill seeker decides to walk to the very edge of the record atradius R. What is the final Moment of Inertia for the system when the bugchanges its position? Assuming that angular momentum is conserved, what isthe final angular speed of the system when the bug has reached the edge? Whatis the bug's linear speed now?Estimate the magnitude of the angular momentum of a bowling ball spinning at 10 rev/s as shown in Fig- ure 11.8. | A typical bowling ball might have a mass of 7.0 kg and a radius of 12 cm.What is the angular momentum of a figure skater spinning at 2.4 rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm , and a mass of 48 kg. How much torque(in magnitude) is required to slow her to a stop in 4.5 s , assuming she does not move her arms?
- 12–158. An airplane is flying in a straight line with a velocity of 200 mi/h and an acceleration of 3 mi/h². If the propeller has a diameter of 6 ft and is rotating at a constant angular rate of 120 rad/s, determine the magnitudes of velocity and acceleration of a particle located on the tip of the propeller.4) try to solve this question, no handwritten12–163. The car travels along the circular curve having a radius r = 400 ft. At the instant shown, its angular rate of rotation is ở = 0.025 rad/s, which is decreasing at the rate ö = -0.008 rad/s². Determine the radial and transverse components of the car's velocity and acceleration at this instant and sketch these components on the curve. *12–164. The car travels along the circular curve of radius r = 400 ft with a constant speed of v = 30 ft/s. Determine the angular rate of rotation ở of the radial line r and the magnitude of the car's acceleration. r= 400 ft
- An amusement park ride (known variously as the Rotor, the Turkish Twist and the Graviton) consists of a large vertical cylinder that is spun about it axis fast enough such that the riders remain pinned against its inner wall. The floor drops away once the cylinder has attained its full rotational speed. The radius of the cylinder is R and the coefficient of static friction between a rider and the wall is us. (i)Show that the minimum FAICT angular speed necessary to keep a rider from falling is given by o = √g/us R. (ii) Obtain a numerical value for frequency in revolutions per minute if R = 4 m and us = 0.4. encloso TOO 07 Fig. Ex. 44; The rotor (an amusement park ride) (For reference only)(II) Suppose our Sun eventually collapses into a white dwarf,losing about half its mass in the process, and winding upwith a radius 1.0% of its existing radius. Assuming the lostmass carries away no angular momentum, (a) what would theSun’s new rotation rate be? Take the Sun’s current period tobe about 30 days. (b) What would be its final kinetic energyin terms of its initial kinetic energy of today?16-146. A ride in an amusement park consists of a rotating arm AB that has an angular acceleration of aдB = 1 rad/s² QAB when @AB = 2 rad/s at the instant shown. Also at this instant the car mounted at the end of the arm has an angular acceleration of a = {-0.6k) rad/s² and angular velocity of w' (-0.5k) rad/s, measured relative to the arm. Determine the velocity and acceleration of the passenger C at this instant. = w' = 0.5 rad/s 10 ft 60° y WAB = 2 rad/s 30° x Probs. 16-145/146 B 2 ft