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A particle of mass 5.0 kg has position vector r = ( 2.0 i ^ 3.0 j ^ ) m at a particular instant of time when its velocity is v = ( 3.0 i ^ ) m / s with respect to the origin. (a) What is the angular momentum of the particle? (b) If a force F = 5.0 j ^ N acts on the particle at this instant, what is the torque about the origin?

a. l = 45.0 kg · m 2 / s k ^ ;
b. τ = 10.0 N · m k ^

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Use the right-hand rule to determine the directions of the angular momenta about the origin of the particles as shown below. The z- axis is out of the page.

Fout particles in the x y plane with different position and velocity vectors are shown. The x and y axes show position in meters and have a range of -4.0 to 4.0 meters. Particle 1 has mass m sub 1, is at x=0 meters and y=2.0 meters, and v sub 1 points in the positive x direction. Particle 2 has mass m sub 2, is at x=2.0 meters and y=-2.0 meters, and v sub 2 point to the right and down, roughly 45 degrees below the positive x direction. Particle 3 has mass m sub 3, is at x=-3.0 meters and y=1.0 meters, and v sub 3 points down, in the negative y direction. Particle 4has mass m sub 4, is at x=4.0 meters and y=0 meters, and v sub 4 points to the left, in the negative x direction.
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Suppose the particles in the preceding problem have masses m 1 = 0.10 kg, m 2 = 0.20 kg, m 3 = 0.30 kg, m 4 = 0.40 kg . The velocities of the particles are v 1 = 2.0 i ^ m / s , v 2 = ( 3.0 i ^ 3.0 j ^ ) m / s , v 3 = −1.5 j ^ m / s , v 4 = −4.0 i ^ m / s . (a) Calculate the angular momentum of each particle about the origin. (b) What is the total angular momentum of the four-particle system about the origin?

a. l 1 = −0.4 kg · m 2 / s k ^ , l 2 = l 4 = 0 ,
l 3 = 1.35 kg · m 2 / s k ^ ; b. L = 0.95 kg · m 2 / s k ^

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Two particles of equal mass travel with the same speed in opposite directions along parallel lines separated by a distance d . Show that the angular momentum of this two-particle system is the same no matter what point is used as the reference for calculating the angular momentum.

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An airplane of mass 4.0 × 10 4 kg flies horizontally at an altitude of 10 km with a constant speed of 250 m/s relative to Earth. (a) What is the magnitude of the airplane’s angular momentum relative to a ground observer directly below the plane? (b) Does the angular momentum change as the airplane flies along its path?

a. L = 1.0 × 10 11 kg · m 2 / s ; b. No, the angular momentum stays the same since the cross-product involves only the perpendicular distance from the plane to the ground no matter where it is along its path.

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At a particular instant, a 1.0-kg particle’s position is r = ( 2.0 i ^ 4.0 j ^ + 6.0 k ^ ) m , its velocity is v = ( −1.0 i ^ + 4.0 j ^ + 1.0 k ^ ) m / s , and the force on it is F = ( 10.0 i ^ + 15.0 j ^ ) N . (a) What is the angular momentum of the particle about the origin? (b) What is the torque on the particle about the origin? (c) What is the time rate of change of the particle’s angular momentum at this instant?

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A particle of mass m is dropped at the point ( d , 0 ) and falls vertically in Earth’s gravitational field g j ^ . (a) What is the expression for the angular momentum of the particle around the z -axis, which points directly out of the page as shown below? (b) Calculate the torque on the particle around the z -axis. (c) Is the torque equal to the time rate of change of the angular momentum?

An x y coordinate system is shown, with positive x to the right and positive y up. A particle is shown on the x axis, to the left of the y axis, at location minus d comma zero. A force minus m g j hat acts downward on the particle.

a. v = g t j ^ , r = d i ^ , l = m d g t k ^ ;
b. F = m g j ^ , τ = d m g k ^ ; c. yes

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(a) Calculate the angular momentum of Earth in its orbit around the Sun. (b) Compare this angular momentum with the angular momentum of Earth about its axis.

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A boulder of mass 20 kg and radius 20 cm rolls down a hill 15 m high from rest. What is its angular momentum when it is half way down the hill? (b) At the bottom?

a. m g h = 1 2 m ( r ω ) 2 + 1 2 2 5 m r 2 ω 2 ;
ω = 51.2 rad / s ;
L = 16.4 kg · m 2 / s ;
b. ω = 72.5 rad / s ;
L = 23.2 kg · m 2 / s

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A satellite is spinning at 6.0 rev/s. The satellite consists of a main body in the shape of a sphere of radius 2.0 m and mass 10,000 kg, and two antennas projecting out from the center of mass of the main body that can be approximated with rods of length 3.0 m each and mass 10 kg. The antenna’s lie in the plane of rotation. What is the angular momentum of the satellite?

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A propeller consists of two blades each 3.0 m in length and mass 120 kg each. The propeller can be approximated by a single rod rotating about its center of mass. The propeller starts from rest and rotates up to 1200 rpm in 30 seconds at a constant rate. (a) What is the angular momentum of the propeller at t = 10 s; t = 20 s? (b) What is the torque on the propeller?

a. I = 720.0 kg · m 2 ; α = 4.20 rad / s 2 ;
ω ( 10 s ) = 42.0 rad / s ; L = 3.02 × 10 4 kg · m 2 / s ;
ω ( 20 s ) = 84.0 rad / s ;
b. τ = 3.03 × 10 3 N · m

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A pulsar is a rapidly rotating neutron star. The Crab nebula pulsar in the constellation Taurus has a period of 33.5 × 10 −3 s , radius 10.0 km, and mass 2.8 × 10 30 kg . The pulsar’s rotational period will increase over time due to the release of electromagnetic radiation, which doesn’t change its radius but reduces its rotational energy. (a) What is the angular momentum of the pulsar? (b) Suppose the angular velocity decreases at a rate of 10 −14 rad / s 2 . What is the torque on the pulsar?

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The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min. (a) If the blades are 6000 kg each and the rotor assembly has three blades, calculate the angular momentum of the turbine at this rotation rate. (b) What is the torque require to rotate the blades up to the maximum rotation rate in 5 minutes?

a. L = 1.131 × 10 7 kg · m 2 / s ;
b. τ = 3.77 × 10 4 N · m

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A roller coaster has mass 3000.0 kg and needs to make it safely through a vertical circular loop of radius 50.0 m. What is the minimum angular momentum of the coaster at the bottom of the loop to make it safely through? Neglect friction on the track. Take the coaster to be a point particle.

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A mountain biker takes a jump in a race and goes airborne. The mountain bike is travelling at 10.0 m/s before it goes airborne. If the mass of the front wheel on the bike is 750 g and has radius 35 cm, what is the angular momentum of the spinning wheel in the air the moment the bike leaves the ground?

ω = 28.6 rad / s L = 2.6 kg · m 2 / s

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Questions & Answers

what is units?
Subhajit Reply
units as in how
praise
What is th formular for force
Joseph Reply
F = m x a
Santos
State newton's second law of motion
Seth Reply
can u tell me I cant remember
Indigo
force is equal to mass times acceleration
Santos
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Asad Reply
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
Sohail Reply
how can one calculate the value of a given quantity
Helen Reply
means?
Manorama
To determine the exact value of a percent of a given quantity we need to express the given percent as fraction and multiply it by the given number.
AMIT
meaning
Winford
briefly discuss rocket in physics
Ibrahim Reply
ok let's discuss
Jay
What is physics
Nura Reply
physics is the study of natural phenomena with concern with matter and energy and relationships between them
Ibrahim
a potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inductance of the inductor that should be connected to the capacitor for the circuit to oscillate at 1125Hza potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inducta
Royalty Reply
L= 0.002H
NNAEMEKA
how did you get it?
Favour
is the magnetic field of earth changing
tibebeab Reply
what is thought to be the energy density of multiverse and is the space between universes really space
tibebeab
can you explain it
Guhan
Energy can not either created nor destroyed .therefore who created? and how did it come to existence?
Suzana Reply
this greatly depend on the kind of energy. for gravitational energy, it is result of the shattering effect violent collision of two black holes on the space-time which caused space time to be disturbed. this is according to recent study on gravitons and gravitational ripple. and many other studies
tibebeab
and not every thing have to pop into existence. and it could have always been there . and some scientists think that energy might have been the only entity in the euclidean(imaginary time T=it) which is time undergone wick rotation.
tibebeab
What is projectile?
Nana Reply
An object that is launched from a device
Grant
2 dimensional motion under constant acceleration due to gravity
Awais
Not always 2D Awais
Grant
no comments
Awais
why not? a bullet is a projectile, so is a rock I throw
Grant
bullet travel in x and y comment same as rock which is 2 dimensional
Awais
components
Awais
no all pf you are wrong. projectile is any object propelled through space by excretion of a force which cease after launch
tibebeab
for awais, there is no such thing as constant acceleration due to gravity, because gravity change from place to place and from different height
tibebeab
it is the object not the motion or its components
tibebeab
where are body center of mass on present.
Balwant Reply
on the mid point
Suzana
is the magnetic field of the earth changing?
tibebeab
does shock waves come to effect when in earth's inner atmosphere or can it have an effect on the thermosphere or ionosphere?
tibebeab
and for the question from bal want do you mean human body or just any object in space
tibebeab
A stone is dropped into a well of 19.6m deep and the impact of sound heared after 2.056 second ,find the velocity of sound in air.
Sisco Reply
9.53 m/s ?
Kyla
In this case, the velocity of sound is 350 m/s.
Zahangir
why?
Kyla
some calculations is need. then you will get exact result.
Zahangir
i mean how? isn't it just a d over t?
Kyla
calculate the time it takes the stone to hit the ground then minus the stone's time to the total time... then divide the total distance by the difference of the time
Snuggly
awit lenard. Hahahah ari ga to!
Kyla
Why do we use mochromatic light? If white light is used, how would the pattern change
Dominic Reply
Practice Key Terms 1

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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