<< Chapter < Page Chapter >> Page >
  • Describe the right-hand rule to find the direction of angular velocity, momentum, and torque.
  • Explain the gyroscopic effect.
  • Study how Earth acts like a gigantic gyroscope.

Angular momentum is a vector and, therefore, has direction as well as magnitude . Torque affects both the direction and the magnitude of angular momentum. What is the direction of the angular momentum of a rotating object like the disk in [link] ? The figure shows the right-hand rule    used to find the direction of both angular momentum and angular velocity. Both L size 12{L} {} and ω size 12{ω} {} are vectors—each has direction and magnitude. Both can be represented by arrows. The right-hand rule defines both to be perpendicular to the plane of rotation in the direction shown. Because angular momentum is related to angular velocity by L = I ω size 12{L=Iω} {} , the direction of L size 12{L} {} is the same as the direction of ω size 12{ω} {} . Notice in the figure that both point along the axis of rotation.

In figure a, a disk is rotating in counter clockwise direction. The direction of the angular momentum is shown as an upward vector at the centre of the disk. The vector is labeled as L is equal to I-omega. In figure b, a right hand is shown. The fingers are curled in the direction of rotation and the thumb is pointed vertically upward in the direction of angular velocity and angular momentum.
Figure (a) shows a disk is rotating counterclockwise when viewed from above. Figure (b) shows the right-hand rule. The direction of angular velocity ω size and angular momentum L are defined to be the direction in which the thumb of your right hand points when you curl your fingers in the direction of the disk’s rotation as shown.

Now, recall that torque changes angular momentum as expressed by

net τ = Δ L Δ t . size 12{"net "τ= { {ΔL} over {Δt} } } {}

This equation means that the direction of Δ L size 12{ΔL} {} is the same as the direction of the torque τ size 12{τ} {} that creates it. This result is illustrated in [link] , which shows the direction of torque and the angular momentum it creates.

Let us now consider a bicycle wheel with a couple of handles attached to it, as shown in [link] . (This device is popular in demonstrations among physicists, because it does unexpected things.) With the wheel rotating as shown, its angular momentum is to the woman's left. Suppose the person holding the wheel tries to rotate it as in the figure. Her natural expectation is that the wheel will rotate in the direction she pushes it—but what happens is quite different. The forces exerted create a torque that is horizontal toward the person, as shown in [link] (a). This torque creates a change in angular momentum L size 12{L} {} in the same direction, perpendicular to the original angular momentum L size 12{L} {} , thus changing the direction of L size 12{L} {} but not the magnitude of L size 12{L} {} . [link] shows how Δ L size 12{ΔL} {} and L size 12{L} {} add, giving a new angular momentum with direction that is inclined more toward the person than before. The axis of the wheel has thus moved perpendicular to the forces exerted on it , instead of in the expected direction.

In figure a, a plane is shown. Force F, lying in the same plane, is acting at a point in the plane. At a point, at distant-r from the force, a vertical vector is shown labeled as tau, the torque. In figure b, there is a child on a horse on a merry-go-round. The radius of the merry-go-round is r units. At the foot of the horse, a vector along the plane of merry-go-round is shown. At the centre, the direction of torque tau, angular velocity omega, and angular momentum L are shown as vertical vectors.
In figure (a), the torque is perpendicular to the plane formed by r size 12{r} {} and F size 12{F} {} and is the direction your right thumb would point to if you curled your fingers in the direction of F size 12{F} {} . Figure (b) shows that the direction of the torque is the same as that of the angular momentum it produces.

In figure a, a lady is holding the spinning bike wheel with her hands. The wheel is rotating in counter clockwise direction. The direction of the force applied by her left hand is shown downward and that by her right hand in upward direction. The direction of angular momentum is along the axis of rotation of the wheel. In figure b, addition of two vectors L and delta-L is shown. The resultant of the two vectors is labeled as L plus delta L. The direction of rotation is counterclockwise.
In figure (a), a person holding the spinning bike wheel lifts it with her right hand and pushes down with her left hand in an attempt to rotate the wheel. This action creates a torque directly toward her. This torque causes a change in angular momentum Δ L in exactly the same direction. Figure (b) shows a vector diagram depicting how Δ L and L add, producing a new angular momentum pointing more toward the person. The wheel moves toward the person, perpendicular to the forces she exerts on it.

Questions & Answers

please I didn't not understand the concept of the physical therapy
John Reply
please I have probably with calculate please can you please and help me out
John Reply
Sure
Gift
What is Boyce law
Sly Reply
how to convert meter per second to kilometers per hour
grace Reply
Divide with 3.6
Mateo
multiply by (km/1000m) x (3600 s/h) -> 3.6
Muhammad
2 how heat loss is prevented in a vacuum flask
Abdullah Reply
what is science
Helen
logical reasoning for a particular phenomenon.
Ajay
I don't know anything about it 😔. I'm sorry, please forgive 😔
Adarsh
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
Lagben Reply
what if time is not given in finding the average velocity?
Alan Reply
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..
Daniel Reply
How do you calculate precision
Sacky Reply
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
lol, hush
Emi
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Bilkisu Reply
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?
Mary Reply
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
Muhammad
when a ball rolls on a smooth level ground,the motion of its centre is?
Mumeh
what's the relationship btw displacement and position
Declan Reply
displacement is the change of position 8======✊=D 💦💦
Anderson
what is the meaning of elasticity
Pele Reply
is the ability of a material to or any object to expand to a limit point
king
this is about kinematics you bonk
Emi
what does emf/R mean
Eze Reply
What is work
Wisdom Reply
work is the product of force and perpendicular distance
DAVID
Practice Key Terms 1

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask