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- University physics volume 1
- Unit 1. mechanics
- Angular momentum
- Angular momentum
Check Your Understanding Which has greater angular momentum: a solid sphere of mass
m rotating at a constant angular frequency
about the
z -axis, or a solid cylinder of same mass and rotation rate about the
z -axis?
; Taking the ratio of the angular momenta, we have:
. Thus, the cylinder has
more angular momentum. This is because the cylinder has more mass distributed farther from the axis of rotation.
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Summary
- The angular momentum
of a single particle about a designated origin is the vector product of the position vector in the given coordinate system and the particle’s linear momentum.
- The angular momentum
of a system of particles about a designated origin is the vector sum of the individual momenta of the particles that make up the system.
- The net torque on a system about a given origin is the time derivative of the angular momentum about that origin:
.
- A rigid rotating body has angular momentum
directed along the axis of rotation. The time derivative of the angular momentum
gives the net torque on a rigid body and is directed along the axis of rotation.
Conceptual questions
For a particle traveling in a straight line, are there any points about which the angular momentum is zero? Assume the line intersects the origin.
All points on the straight line will give zero angular momentum, because a vector crossed into a parallel vector is zero.
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If a particle is moving with respect to a chosen origin it has linear momentum. What conditions must exist for this particle’s angular momentum to be zero about the chosen origin?
The particle must be moving on a straight line that passes through the chosen origin.
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Problems
A bird flies overhead from where you stand at an altitude of 300.0 m and at a speed horizontal to the ground of 20.0 m/s. The bird has a mass of 2.0 kg. The radius vector to the bird makes an angle
with respect to the ground. The radius vector to the bird and its momentum vector lie in the
xy -plane. What is the bird’s angular momentum about the point where you are standing?
The magnitude of the cross product of the radius to the bird and its momentum vector yields
, which gives
as the altitude of the bird
h . The direction of the angular momentum is perpendicular to the radius and momentum vectors, which we choose arbitrarily as
, which is in the plane of the ground:
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A Formula One race car with mass 750.0 kg is speeding through a course in Monaco and enters a circular turn at 220.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 180 km/h also in the counterclockwise direction. If the radius of curvature of the first turn is 130.0 m and that of the second is 100.0 m, compare the angular momenta of the race car in each turn taken about the origin of the circular turn.
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Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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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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