FUNDAMENTALS OF PHYSICS V.1
11th Edition
ISBN: 9781119573913
Author: Halliday
Publisher: WILEY
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Chapter 10, Problem 62P
In Fig. 10-35, three 0.0100 kg particles have been glued to a rod of length L = 6.00 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to rad/s. (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly’s kinetic energy (in joules) versus the square of its rotation rate (in radians- squared per second-squared)?
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
seconds. If the radius of the wheel is 400mm. calculate
ii)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
Question 04
in 20
Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 10 Solutions
FUNDAMENTALS OF PHYSICS V.1
Ch. 10 - Figure 10-20 is a graph of the angular velocity...Ch. 10 - Figure 10-21 shows plots of angular position ...Ch. 10 - A force is applied to the rim of a disk that can...Ch. 10 - Figure 10-22b is a graph of the angular position...Ch. 10 - In Fig. 10-23, two forces F1 and F2 act on a disk...Ch. 10 - In the overhead view of Fig. 10-24, five forces of...Ch. 10 - Figure 10-25a is an overhead view of a horizontal...Ch. 10 - Figure l0-25b shows an overhead view of a...Ch. 10 - Figure 10-26 shows a uniform metal plate that had...Ch. 10 - Figure 10-27 shows three flat disks of the same...
Ch. 10 - Figure 10-28a shows a meter stick, hall wood and...Ch. 10 - Figure 10-29 shows three disks, each with a...Ch. 10 - A good baseball pitcher can throw a baseball...Ch. 10 - What is the angular speed of a the second hand, b...Ch. 10 - When a slice of buttered toast is accidentally...Ch. 10 - The angular position of a point on a rotating...Ch. 10 - ILW A diver makes 2.5 revolutions on the way from...Ch. 10 - The angular position of a point on the rim of a...Ch. 10 - The wheel in Fig. 10-30 has eight equally spaced...Ch. 10 - The angular acceleration of a wheel is = 6.0t4 ...Ch. 10 - A drum rotates around its central axis at an...Ch. 10 - Starting from rest, a disk rotates about its...Ch. 10 - A disk, initially rotating at 120 rad/s, is slowed...Ch. 10 - The angular speed of an automobile engine is...Ch. 10 - ILW A flywheel turns through 40 rev as it slows...Ch. 10 - GO A disk rotates about its central axis starling...Ch. 10 - SSM Starting from rest, a wheel has constant =...Ch. 10 - A merry-go-round rotates from rest with an angular...Ch. 10 - At t = 0, a flywheel has an angular velocity of...Ch. 10 - A pulsar is a rapidly rotating neutron star that...Ch. 10 - What are the magnitudes of a the angular velocity,...Ch. 10 - An object rotates about a fixed axis, and the...Ch. 10 - Between 1911 and 1990, the top of the leaning bell...Ch. 10 - An astronaut is tested in a centrifuge with radius...Ch. 10 - SSM WWW A flywheel with a diameter of 1.20 m is...Ch. 10 - A vinyl record is played by rotating the record so...Ch. 10 - SSM a What is the angular speed about the polar...Ch. 10 - The flywheel of a steam engine runs with a...Ch. 10 - A seed is on a turntable rotating at 3313 rev/min,...Ch. 10 - In Fig. 10-31, wheel A of radius rA = 10 cm is...Ch. 10 - Figure 10-32 shows an early method of measuring...Ch. 10 - A gyroscope flywheel of radius 2.83 cm is...Ch. 10 - GO A disk, with a radius of 0.25 m. is to be...Ch. 10 - A car starts from rest and moves around a circular...Ch. 10 - SSM Calculate the rotational inertia of a wheel...Ch. 10 - Figure 10-33 gives angular speed versus time for a...Ch. 10 - SSM Two uniform solid cylinders, each rotating...Ch. 10 - Figure 10-34a shows a disk that can rotate about...Ch. 10 - SSM Calculate the rotational inertia of a meter...Ch. 10 - Figure 10-35 shows three 0.0100 kg particles that...Ch. 10 - Trucks can be run on energy stored in a rotating...Ch. 10 - Figure 10-36 shows an arrangement of 15 identical...Ch. 10 - GO In Fig. 10-37, two particles, each with mass m...Ch. 10 - The masses and coordinates of four particles are...Ch. 10 - SSM WWW The uniform solid block in Fig. 10-38 has...Ch. 10 - Four identical particles of mass 0.50 kg each are...Ch. 10 - SSM ILW The body in Fig. 10-39 is pivoted at O,...Ch. 10 - The body in Fig. 10-40 is pivoted at O. Three...Ch. 10 - SSM A small ball of mass 0.75 kg is attached to...Ch. 10 - The length of a bicycle pedal arm is 0.152 m, and...Ch. 10 - SSM ILW During the launch from a board, a divers...Ch. 10 - If a 32.0 N m torque on a wheel causes angular...Ch. 10 - Prob. 51PCh. 10 - GO In Fig. 10-42, a cylinder having a mass of 2.0...Ch. 10 - GO Figure 10-43 shows a uniform disk that can...Ch. 10 - In a judo foot-sweep move, you sweep your...Ch. 10 - In Fig. 10-45a, an irregularly shaped plastic...Ch. 10 - Figure 10-46 shows particles 1 and 2, each of mass...Ch. 10 - GO A pulley, with a rotational inertia of 1.0 103...Ch. 10 - a IF R= 12 cm, M = 400 g, and m = 50 g in Fig....Ch. 10 - An automobile crankshaft transfers energy from the...Ch. 10 - A thin rod of length 0.75 m and mass 0.42 kg is...Ch. 10 - A 32.0 kg wheel, essentially a thin hoop with...Ch. 10 - In Fig. 10-35, three 0.0100 kg particles have been...Ch. 10 - SSM ILW A meter stick is held vertically with one...Ch. 10 - A uniform cylinder of radius 10 cm and mass 20 kg...Ch. 10 - GO A tall, cylindrical chimney fall;; over when...Ch. 10 - GO A uniform spherical shell of mass M = 4.5 kg...Ch. 10 - GO Figure 10-48 shows a rigid assembly of a thin...Ch. 10 - Prob. 68PCh. 10 - Prob. 69PCh. 10 - A wheel, starling from rest, rotates with a...Ch. 10 - SSM In Fig. 10-50, two 6.20 kg blocks are...Ch. 10 - Prob. 72PCh. 10 - A uniform helicopter rotor blade is 7.80 m long,...Ch. 10 - Prob. 74PCh. 10 - Prob. 75PCh. 10 - Starting from rest at t = 0, a wheel undergoes a...Ch. 10 - SSM A record turntable rotating at 3313 rev/min...Ch. 10 - Prob. 78PCh. 10 - Prob. 79PCh. 10 - A disk rotates al constant angular acceleration,...Ch. 10 - GO The thin uniform rod in Fig. 10-53 has length...Ch. 10 - Prob. 82PCh. 10 - Prob. 83PCh. 10 - At 7:14 A.M. on June 30, 1908, a huge explosion...Ch. 10 - A golf ball is launched at an angle of 20 to the...Ch. 10 - Prob. 86PCh. 10 - GO IN Fig. 10-55, a wheel of radius 0.20 m is...Ch. 10 - A thin spherical shell has a radius of 1.90 m. An...Ch. 10 - Prob. 89PCh. 10 - The flywheel of an engine is rotating at 25.0...Ch. 10 - SSM In Fig. 10-19a, a wheel of radius 0.20 m is...Ch. 10 - Our Sun is 23 104 ly light-years from the center...Ch. 10 - SSM A wheel of radius 0.20 m is mounted on a...Ch. 10 - If an airplane propeller rotates at 2000 rev/min...Ch. 10 - The rigid body shown in Fig. 10-57 consists of...Ch. 10 - Beverage engineering. The pull tab was a major...Ch. 10 - Figure 10-58 shows a propeller blade that rotates...Ch. 10 - A yo-yo-shaped device mounted on a horizontal...Ch. 10 - Prob. 99PCh. 10 - Two thin rods each of mass 0.20 kg are joined...Ch. 10 - In Fig. 10-61, four pulleys are connected by two...Ch. 10 - Prob. 102PCh. 10 - In Fig. 10-63, a thin uniform rod mass 3.0 kg,...Ch. 10 - Prob. 104PCh. 10 - Prob. 105PCh. 10 - A point on the rim of a 0.75-m-diameler grinding...Ch. 10 - A pulley wheel that is 8.0 cm in diameter has a...Ch. 10 - A vinyl record on a turntable rotates at 3313...
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