Physics
7th Edition
ISBN: 9780321625915
Author: Douglas C. Giancoli
Publisher: PEARSON
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Chapter 8, Problem 14P
(a)
To determine
The
(b)
To determine
The components of the linear acceleration of a point on the edge of the wheel
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Sketch the harmonic.
Chapter 8 Solutions
Physics
Ch. 8 - A solid ball and a solid cylinder roll down a...Ch. 8 - A bicycle odometer (which counts revolutions and...Ch. 8 - Prob. 2QCh. 8 - Prob. 3QCh. 8 - Why is it more difficult to do a sit-up with your...Ch. 8 - If the net force on a system is zero, is the net...Ch. 8 - Mammals that depend on being able to run fast have...Ch. 8 - This book has three symmetry axes through its...Ch. 8 - Can the mass of a rigid object be considered...Ch. 8 - The moment of inertia of a rotating solid disk...
Ch. 8 - Two inclines have the same height but make...Ch. 8 - Two spheres look identical and have the same mass....Ch. 8 - A sphere and a cylinder have the same radius and...Ch. 8 - Prob. 13QCh. 8 - Prob. 14QCh. 8 - 15. Can the diver of Fig. 8-28 do a somersault...Ch. 8 - When a motorcyclist leaves the ground on a jump...Ch. 8 - Prob. 17QCh. 8 - 18. The angular velocity of a wheel rotating on a...Ch. 8 - 19. In what direction is the Earth's angular...Ch. 8 - 20. ‘On the basis of the law of conservation of...Ch. 8 - Bonnie sits on the outer rim of a merry-go-round,...Ch. 8 - Prob. 2MCQCh. 8 - Prob. 3MCQCh. 8 - Prob. 4MCQCh. 8 - Prob. 5MCQCh. 8 - Prob. 6MCQCh. 8 - Prob. 7MCQCh. 8 - Prob. 8MCQCh. 8 - Prob. 9MCQCh. 8 - Prob. 10MCQCh. 8 - Prob. 11MCQCh. 8 - Prob. 12MCQCh. 8 - Suppose you are sitting on a rotating stool...Ch. 8 - Express the following angles in radians: (a)...Ch. 8 - The Sun subtends an angle of about 0.5° to us on...Ch. 8 - A laser beam is directed at the Moon, 380,000 km...Ch. 8 - The blades in a blender rotate at a rate of 6500...Ch. 8 - 5. (II) The platter of the hard drive of a...Ch. 8 - Prob. 6PCh. 8 - (a) A grinding wheel 0.35 m in diameter rotates at...Ch. 8 - Prob. 8PCh. 8 - Calculate the angular velocity (a) of a clock's...Ch. 8 - Prob. 10PCh. 8 - What is the linear speed, due to the Earth's...Ch. 8 - Prob. 12PCh. 8 - How fast (in rpm) must a centrifuge rotate ifa...Ch. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - An automobile engine slows down from 3500 rpm to...Ch. 8 - 18. (I) A centrifuge accelerates uniformly from...Ch. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - A wheel 31 cm in diameter accelerates uniformly...Ch. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - A 52-kg person riding a bike puts all her weight...Ch. 8 - Calculate the net torque about the axle of the...Ch. 8 - A person exerts a horizontal force of 42 N on the...Ch. 8 - Prob. 27PCh. 8 - The bolts on the cylinder head of an engine...Ch. 8 - Determine the net torque on the 2.0-m-long uniform...Ch. 8 - Determine the moment of inertia of a 10.8-kg...Ch. 8 - 31. (I) Estimate the moment of inertia of a...Ch. 8 - A merry-go-round accelerates from rest to 0.68...Ch. 8 - Prob. 33PCh. 8 - (II) A grinding wheel is a uniform cylinder with a...Ch. 8 - Prob. 35PCh. 8 - Prob. 36PCh. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - Prob. 39PCh. 8 - Prob. 40PCh. 8 - Prob. 41PCh. 8 - Prob. 42PCh. 8 - Prob. 43PCh. 8 - A centrifuge rotor rotating at 9200 rpm is shut...Ch. 8 - 45. (II) To get a flat, uniform cylindrical...Ch. 8 - 46. (Ill) Two blocks are connected by a light...Ch. 8 - 47 (III) An Atwood machine consists of two masses,...Ch. 8 - A hammer thrower accelerates the hammer (mass...Ch. 8 - 49. (I) An automobile engine develops a torque of...Ch. 8 - A centrifuge rotor has a moment of inertia of 325...Ch. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - Prob. 55PCh. 8 - Prob. 56PCh. 8 - Prob. 57PCh. 8 - Prob. 58PCh. 8 - Prob. 59PCh. 8 - What is the angular momentum of a 0.270-kg ball...Ch. 8 - (a) What is the angular momentum of a 2.8-kg...Ch. 8 - Prob. 62PCh. 8 - Prob. 63PCh. 8 - Prob. 64PCh. 8 - Prob. 65PCh. 8 - Prob. 66PCh. 8 - A person of mass 75 kg stands at the center of a...Ch. 8 - Prob. 68PCh. 8 - Prob. 69PCh. 8 - Prob. 70PCh. 8 - Prob. 71PCh. 8 - Prob. 72PCh. 8 - Prob. 73PCh. 8 - Prob. 74PCh. 8 - Prob. 75GPCh. 8 - Prob. 76GPCh. 8 - Prob. 77GPCh. 8 - Prob. 78GPCh. 8 - Prob. 79GPCh. 8 - Prob. 80GPCh. 8 - Prob. 81GPCh. 8 - Figure 8-59 illustrates an H20 molecule The O — H...Ch. 8 - A hollow cylinder (hoop) is rolling on a...Ch. 8 - Prob. 84GPCh. 8 - Prob. 85GPCh. 8 - Prob. 86GPCh. 8 - Prob. 87GPCh. 8 - Prob. 88GPCh. 8 - Prob. 89GPCh. 8 - Prob. 90GPCh. 8 - A large spool of rope rolls on the ground with the...Ch. 8 - The Moon orbits the Earth such that the same side...Ch. 8 - Prob. 93GPCh. 8 - Most of our Solar System's mass is contained in...Ch. 8 - Prob. 95GPCh. 8 - Prob. 96GP
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