# 10.5 Angular momentum and its conservation  (Page 4/7)

 Page 4 / 7

Solution for (b)

Rotational kinetic energy is given by

${\text{KE}}_{\text{rot}}=\frac{1}{2}{\mathrm{I\omega }}^{2}.$

The initial value is found by substituting known values into the equation and converting the angular velocity to rad/s:

$\begin{array}{lll}{\text{KE}}_{\text{rot}}& =& \left(0\text{.}5\right)\left(2\text{.}\text{34}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot {\text{m}}^{2}\right){\left(\left(0\text{.}\text{800}\phantom{\rule{0.25em}{0ex}}\text{rev/s}\right)\left(2\pi \phantom{\rule{0.25em}{0ex}}\text{rad/rev}\right)\right)}^{2}\\ & =& 29.6\phantom{\rule{0.25em}{0ex}}\text{J.}\end{array}$

The final rotational kinetic energy is

${\text{KE}}_{\text{rot}}\prime =\frac{1}{2}I\prime {\omega \prime }^{2}.$

Substituting known values into this equation gives

$\begin{array}{lll}K{E}_{\text{rot}}\prime & =& \left(0\text{.}5\right)\left(0\text{.363 kg}\cdot {m}^{2}\right){\left[\left(5\text{.}\text{16 rev/s}\right)\left(2\pi rad/rev\right)\right]}^{2}\\ & =& \text{191 J.}\end{array}$

Discussion

In both parts, there is an impressive increase. First, the final angular velocity is large, although most world-class skaters can achieve spin rates about this great. Second, the final kinetic energy is much greater than the initial kinetic energy. The increase in rotational kinetic energy comes from work done by the skater in pulling in her arms. This work is internal work that depletes some of the skater’s food energy.

There are several other examples of objects that increase their rate of spin because something reduced their moment of inertia. Tornadoes are one example. Storm systems that create tornadoes are slowly rotating. When the radius of rotation narrows, even in a local region, angular velocity increases, sometimes to the furious level of a tornado. Earth is another example. Our planet was born from a huge cloud of gas and dust, the rotation of which came from turbulence in an even larger cloud. Gravitational forces caused the cloud to contract, and the rotation rate increased as a result. (See [link] .)

In case of human motion, one would not expect angular momentum to be conserved when a body interacts with the environment as its foot pushes off the ground. Astronauts floating in space aboard the International Space Station have no angular momentum relative to the inside of the ship if they are motionless. Their bodies will continue to have this zero value no matter how they twist about as long as they do not give themselves a push off the side of the vessel.

Is angular momentum completely analogous to linear momentum? What, if any, are their differences?

Yes, angular and linear momentums are completely analogous. While they are exact analogs they have different units and are not directly inter-convertible like forms of energy are.

## Section summary

• Every rotational phenomenon has a direct translational analog , likewise angular momentum $L$ can be defined as $L=\mathrm{I\omega }.$
• This equation is an analog to the definition of linear momentum as $p=\text{mv}$ . The relationship between torque and angular momentum is $\text{net}\phantom{\rule{0.25em}{0ex}}\tau =\frac{\text{Δ}L}{\text{Δ}t}.$
• Angular momentum, like energy and linear momentum, is conserved. This universally applicable law is another sign of underlying unity in physical laws. Angular momentum is conserved when net external torque is zero, just as linear momentum is conserved when the net external force is zero.

## Conceptual questions

When you start the engine of your car with the transmission in neutral, you notice that the car rocks in the opposite sense of the engine’s rotation. Explain in terms of conservation of angular momentum. Is the angular momentum of the car conserved for long (for more than a few seconds)?

Suppose that a grandfather clock is running slowly; that is, the time it takes to complete each cycle is longer than it should be. Should you (@) shorten or (b) lengthen the pendulam to make the clock keep attain the preferred time?
I think you shorten am not sure
Uche
discuss under damped
resistance of thermometer in relation to temperature
how
Bernard
that resistance is not measured yet, it may be probably in the next generation of scientists
Paul
Is fundamental quantities under physical quantities?
please I didn't not understand the concept of the physical therapy
physiotherapy - it's a practice of exercising for healthy living.
Paul
what chapter is this?
Anderson
this is not in this book, it's from other experiences.
Paul
Sure
What is Boyce law
how to convert meter per second to kilometers per hour
Divide with 3.6
Mateo
multiply by (km/1000m) x (3600 s/h) -> 3.6
2 how heat loss is prevented in a vacuum flask
what is science
Helen
logical reasoning for a particular phenomenon.
Ajay
I don't know anything about it 😔. I'm sorry, please forgive 😔
due to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask
Abdul
dimensions v²=u²+2at
what if time is not given in finding the average velocity?
the magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber/m is to produce in the magnet of 1500 turns..
How do you calculate precision
what module is that?
Fillemon
Chemisty 1A?
Fillemon
No it has something to do with measurements bro... What we did today in class
Sacky
Tah bra honestly I didn't understand a thing in that class..when re your Tutorials?
Fillemon
Friday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet
Sacky
I eat ass
Anderson
I'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them
Fillemon
I'll eat your mom's ass with a side of tendies
Anderson
@Fillemon Nanwaapo
Anderson
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Emi
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Because there's an equal number of negative and positive charges... objects are neutral in nature
NELSON
when a ball rolls on a smooth level ground,the motion of its centre is?
what is electro magnetic field?
Mary
electromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!
NELSON
Electromagnetic field is caused by moving electric charge
when a ball rolls on a smooth level ground,the motion of its centre is?
Mumeh