PHYSICS:F/SCI.+ENGRS.(LL)-W/WEBASSIGN
10th Edition
ISBN: 9781337888714
Author: SERWAY
Publisher: CENGAGE L
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Chapter 15, Problem 29P
(a)
To determine
The moment of inertia of the probe about its center of mass.
(b)
To determine
The value of moment of inertia is too low or too high.
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Question 3 of 17
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In the figure above, three uniform thin rods, each of length L, form
an inverted U. The vertical rods each have a mass m; the horizontal
rod has a mass 3m.
NOTE: Express your answer in terms of the variables given.
(a) What is the x coordinate of the system's center of mass?
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(b) What is the y coordinate of the system's center of mass?
Ycom
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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
Chapter 15 Solutions
PHYSICS:F/SCI.+ENGRS.(LL)-W/WEBASSIGN
Ch. 15.1 - A block on the end of a spring is pulled to...Ch. 15.2 - Consider a graphical representation (Fig. 15.3) of...Ch. 15.2 - Figure 15.4 shows two curves representing...Ch. 15.2 - An object of mass m is hung from a spring and set...Ch. 15.4 - The ball in Figure 15.13 moves in a circle of...Ch. 15.5 - The grandfather clock in the opening storyline...Ch. 15 - A 0.60-kg block attached to a spring with force...Ch. 15 - A piston in a gasoline engine is in simple...Ch. 15 - The position of a particle is given by the...Ch. 15 - A 7.00-kg object is hung from the bottom end of a...
Ch. 15 - Review. A particle moves along the x axis. It is...Ch. 15 - A ball dropped from a height of 4.00 m makes an...Ch. 15 - A particle moving along the x axis in simple...Ch. 15 - The initial position, velocity, and acceleration...Ch. 15 - You attach an object to the bottom end of a...Ch. 15 - To test the resiliency of its bumper during...Ch. 15 - A particle executes simple harmonic motion with an...Ch. 15 - The amplitude of a system moving in simple...Ch. 15 - A simple harmonic oscillator of amplitude A has a...Ch. 15 - Review. A 65.0-kg bungee jumper steps off a bridge...Ch. 15 - Review. A 0.250-kg block resting on a...Ch. 15 - While driving behind a car traveling at 3.00 m/s,...Ch. 15 - A simple pendulum makes 120 complete oscillations...Ch. 15 - A particle of mass m slides without friction...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - Prob. 21PCh. 15 - Consider the physical pendulum of Figure 15.16....Ch. 15 - A watch balance wheel (Fig. P15.25) has a period...Ch. 15 - Show that the time rate of change of mechanical...Ch. 15 - Show that Equation 15.32 is a solution of Equation...Ch. 15 - As you enter a fine restaurant, you realize that...Ch. 15 - A 2.00-kg object attached to a spring moves...Ch. 15 - Considering an undamped, forced oscillator (b =...Ch. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - An object of mass m moves in simple harmonic...Ch. 15 - Review. This problem extends the reasoning of...Ch. 15 - An object attached to a spring vibrates with...Ch. 15 - Review. A rock rests on a concrete sidewalk. An...Ch. 15 - A pendulum of length L and mass M has a spring of...Ch. 15 - To account for the walking speed of a bipedal or...Ch. 15 - Review. A particle of mass 4.00 kg is attached to...Ch. 15 - People who ride motorcycles and bicycles learn to...Ch. 15 - A ball of mass m is connected to two rubber bands...Ch. 15 - Consider the damped oscillator illustrated in...Ch. 15 - Review. A lobstermans buoy is a solid wooden...Ch. 15 - Your thumb squeaks on a plate you have just...Ch. 15 - Prob. 43APCh. 15 - Prob. 44APCh. 15 - A block of mass m is connected to two springs of...Ch. 15 - Review. A light balloon filled with helium of...Ch. 15 - A particle with a mass of 0.500 kg is attached to...Ch. 15 - A smaller disk of radius r and mass m is attached...Ch. 15 - Review. A system consists of a spring with force...Ch. 15 - Review. Why is the following situation impassible?...Ch. 15 - A light, cubical container of volume a3 is...
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