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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.

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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.

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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?

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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} {}

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Questions & Answers

write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
what is vector quantity
Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
Jack Reply
what's electromagnetic induction
Chinaza Reply
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
wow great
Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
Ajayi Reply
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
Gabriel Reply
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
Gabriel Reply
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
Ademiye
yes it was an assignment question "^"represent raise to power pls
Gabriel
mu/y³ u>v²k² uk²/√u-vk please help me out
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
Imtiaz Reply
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Ademiye
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
Isaac Reply
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
Mildred Reply
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
Ademiye
method of polarization
Ajayi
What is atomic number?
Makperr Reply
The number of protons in the nucleus of an atom
Deborah
type of thermodynamics
Yinka Reply
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
Taheer Reply
why the satellite does not drop to the earth explain
Emmanuel Reply
what is a matter
Yinka
what is matter
Yinka
what is matter
Yinka
what is a matter
Yinka
I want the nuclear physics conversation
Mohamed
because space is a vacuum and anything outside the earth 🌎 can not come back without an act of force applied to it to leave the vacuum and fall down to the earth with a maximum force length of 30kcm per second
Clara
Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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