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This same logic explains the behavior of gyroscopes. [link] shows the two forces acting on a spinning gyroscope. The torque produced is perpendicular to the angular momentum, thus the direction of the torque is changed, but not its magnitude. The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular to L size 12{L} {} . If the gyroscope is not spinning, it acquires angular momentum in the direction of the torque ( L = Δ L size 12{L=ΔL} {} ), and it rotates around a horizontal axis, falling over just as we would expect.

Earth itself acts like a gigantic gyroscope. Its angular momentum is along its axis and points at Polaris, the North Star. But Earth is slowly precessing (once in about 26,000 years) due to the torque of the Sun and the Moon on its nonspherical shape.

In figure a, the gyroscope is rotating in counter clockwise direction. The weight of the gyroscope is acting downward. The supportive force is acting at the base. The line of action of the weight and supportive force are different. The torque is acting along the radius of the horizontal circular part of gyroscope. In figure b, the two vectors L and L plus delta L are shown. The vectors start from a point at the bottom of the figure and terminate at two points on a horizontal dotted circle, directed in counter clockwise direction, at the top of the figure. Another vector delta L starts from the head of vector L and terminates at the head of vector L plus delta L.
As seen in figure (a), the forces on a spinning gyroscope are its weight and the supporting force from the stand. These forces create a horizontal torque on the gyroscope, which create a change in angular momentum Δ L size 12{L} {} that is also horizontal. In figure (b), Δ L size 12{L} {} and L size 12{L} {} add to produce a new angular momentum with the same magnitude, but different direction, so that the gyroscope precesses in the direction shown instead of falling over.

Rotational kinetic energy is associated with angular momentum? Does that mean that rotational kinetic energy is a vector?

No, energy is always a scalar whether motion is involved or not. No form of energy has a direction in space and you can see that rotational kinetic energy does not depend on the direction of motion just as linear kinetic energy is independent of the direction of motion.

Section summary

  • 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 if you curled the fingers of your right hand in the direction of F size 12{F} {} . The direction of the torque is thus the same as that of the angular momentum it produces.
  • The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular to L size 12{L} {} . If the gyroscope is not spinning, it acquires angular momentum in the direction of the torque ( L = Δ L size 12{L=ΔL} {} ), and it rotates about a horizontal axis, falling over just as we would expect.
  • Earth itself acts like a gigantic gyroscope. Its angular momentum is along its axis and points at Polaris, the North Star.

Conceptual questions

While driving his motorcycle at highway speed, a physics student notices that pulling back lightly on the right handlebar tips the cycle to the left and produces a left turn. Explain why this happens.

Gyroscopes used in guidance systems to indicate directions in space must have an angular momentum that does not change in direction. Yet they are often subjected to large forces and accelerations. How can the direction of their angular momentum be constant when they are accelerated?

Problem exercises

Integrated Concepts

The axis of Earth makes a 23.5° angle with a direction perpendicular to the plane of Earth’s orbit. As shown in [link] , this axis precesses, making one complete rotation in 25,780 y.

(a) Calculate the change in angular momentum in half this time.

(b) What is the average torque producing this change in angular momentum?

(c) If this torque were created by a single force (it is not) acting at the most effective point on the equator, what would its magnitude be?

In the figure, the Earth’s image is shown. There are two vectors inclined at an angle of twenty three point five degree to the vertical, starting from the centre of the Earth. At the heads of the two vectors there is a circular shape, directed in counter clockwise direction. An angular momentum vector, directed toward left, along its diameter, is shown. The plane of the Earth’s orbit is shown as a horizontal line through its center.
The Earth’s axis slowly precesses, always making an angle of 23.5° with the direction perpendicular to the plane of Earth’s orbit. The change in angular momentum for the two shown positions is quite large, although the magnitude L size 12{L} {} is unchanged.

(a) 5 . 64 × 10 33 kg m 2 /s size 12{5 "." "65" times "10" rSup { size 8{"33"} } `"kg" "." m rSup { size 8{2} } "/s"} {}

(b) 1 . 39 × 10 22 N m size 12{1 "." "39" times "10" rSup { size 8{"22"} } `N cdot m} {}

(c) 2 . 17 × 10 15 N size 12{2 "." "18" times "10" rSup { size 8{"15"} } `N} {}

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Mueller Reply
How we can toraidal magnetic field
Aditya Reply
How we can create polaidal magnetic field
Aditya
4
Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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