What is Rotational energy: Definition and 108 Discussions
Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed:
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{\displaystyle E_{\mathrm {rotational} }={\frac {1}{2}}I\omega ^{2}}
where
ω
{\displaystyle \omega \ }
is the angular velocity
I
{\displaystyle I\ }
is the moment of inertia around the axis of rotation
E
{\displaystyle E\ }
is the kinetic energyThe mechanical work required for or applied during rotation is the torque times the rotation angle. The instantaneous power of an angularly accelerating body is the torque times the angular velocity. For free-floating (unattached) objects, the axis of rotation is commonly around its center of mass.
Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:
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{\displaystyle E_{\mathrm {translational} }={\frac {1}{2}}mv^{2}}
In the rotating system, the moment of inertia, I, takes the role of the mass, m, and the angular velocity,
ω
{\displaystyle \omega }
, takes the role of the linear velocity, v. The rotational energy of a rolling cylinder varies from one half of the translational energy (if it is massive) to the same as the translational energy (if it is hollow).
An example is the calculation of the rotational kinetic energy of the Earth. As the Earth has a period of about 23.93 hours, it has an angular velocity of 7.29×10−5 rad/s. The Earth has a moment of inertia, I = 8.04×1037 kg·m2. Therefore, it has a rotational kinetic energy of 2.138×1029 J.
A good example of actually using earth's rotational energy is the location of the European spaceport in French Guiana. This is within about 5 degrees of the equator, so space rocket launches (for primarily geo-stationary satellites) from here to the east obtain nearly all of the full rotational speed of the earth at the equator (about 1,000 mph, sort of a "sling-shot" benefit). This saves significant rocket fuel per launch compared with rocket launches easterly from Kennedy Space Center (USA), which obtain only about 900 mph added benefit due to the lower relative rotational speed of the earth at that northerly latitude of 28 degrees.
Part of the earth's rotational energy can also be tapped using tidal power. Additional friction of the two global tidal waves creates energy in a physical manner, infinitesimally slowing down Earth's angular velocity ω. Due to the conservation of angular momentum, this process transfers angular momentum to the Moon's orbital motion, increasing its distance from Earth and its orbital period (see tidal locking for a more detailed explanation of this process).
Because it rotates around its axis, then it has a rotational kinetic energy. But when it orbits the Sun, then it has an another rotational energy too. Would it be ##E_\mathrm{rot} = \frac 12 (\frac 25 MR^2+ Md^2) {\omega}^2 ##, where ##d## is the distance between the Sun and the Earth. I...
I am a bit confused with velocities in this problem. From Philipp's view, the coin's initial velocity is zero, so its transfer kinetic energy is also zero. When I am standing on a non-moving ground, is the coin's initial velocity ##v## in direction the walkway is moving? But won't I get then...
Given that there is a cylinder rolling without slipping down an incline, the method I was taught to represent the KE of the cylinder was:
##KE_{total} = KE_{translational} + KE_{rotational}##
##KE_{total} = \frac {1} {2} mv_{cm}^2 + \frac1 2 I \omega^2## Where "cm" is the center of mass, and...
A carousel has the shape of a circular disc with radius 1.80 m and a mass of 300 kg. There are two people with masses of 30 and 45 kg out on the edge while carousel rotates with the angular speed 0.6 rad / s.
The people move towards the center of the carousel
Calculations show that the...
When does an object have rotational energy? Is it only if it rotates around an axis within the object? Does for example a ball attached to a string with a uniform circular movement have rotational kinetic energy?
Summary: I want to show by using the rotational energy formula that ##E(2^+) = 92 KeV##? But I got ##E(2^+) = 3096KeV##. Below is what I've done. There must be something I am missing.
[Moderator's note: Moved from a technical forum and thus no template.]
There is a cornering maneuver in rallying called the "Scandinavian flick" or the "pendulum turn". It involves steering away from the corner before actually steering into the corner. This creates a pendulum effect which makes the car turn more sharply into the corner.
Sorry for the poor video...
I found one answer somewhere else in the internet, It specified there that atoms cannot have rotational and vibrational energies since they don't have a point on them that will allow the atom to be rotated or vibrated. However , that answer did not suffice so I ask the same question here.
If I have a DC induction motor coil of a zero resistance so that means that to sustain a constant magnetic field I do not need any energy. So in a DC motor how is energy of zero resistance circuit converted to rotational energy of a motor?
So I found the linear velocity by using the circumference of the Earth which I found to be 2pi(637800= 40014155.89meters. Then the time of one full rotation was 1436.97 minutes, which I then converted to 86164.2 seconds. giving me the linear velocity to be 465.0905584 meters/second. I know that...
Hello!
What are the available methods to harvest rotational energy?
I was thinking to put a turbine on the shaft and compress air, but the air will get cold and the energy will be lost.
I was thinking to put an electric generator, which is ok but it needs a battery.
I was thinking to use...
Hi!
I am making an aeolipile as a school project, and I was wondering if you could calculate the rpm.
This is the basic principle of an aeolipile.
You should be able to calculate the rotating velocity right? Knowing the mass and ignoring any resistance.
But then you'll need the rotating...
Homework Statement
A school playground has a carousel, which is simply a circular platform that can rotate around its center axis with negligible friction. This carousel has radius r=1.6 m and rotational inertia I= 177m^2kg. Suppose you are standing beside the carousel which is already spinning...
Homework Statement
The marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off? (Use any variable or symbol stated above along with the...
Homework Statement
The rotational spectrum of HCl contains the following wavelengths:
12.03 10 5 m 9.60 10 5 m 8.04 10 5 m 6.89 10 5 m 6.04 10 5 m
If the isotopes involved are 1H and 35Cl, find the distance between the hydrogen and chlorine nuclei in an HCl molecule.
Homework Equations
E...
Homework Statement
Determines the average energy of rotation (per molecule) of a rarefied gas of HF at T = 50 K, knowing that the wave number of rotational absorption for the transition L = 2 → 3 worth 121.5 cm-1. [Hint: it performs the calculation by limiting the number of levels taken into...
Homework Statement
From an İnitial Lenght h,a solid ball rolls smoothly down one side of a U-shaped ramp and then moves up the other side,which is frictionless.What maximum height does the ball reach ?
Homework Equations
Energy conservation equations
The Attempt at a Solution...
Homework Statement
A Verdant Power water turbine (a “windmill” in water) turns in the East River near New York City. Its propeller is 2.5 m in radius and spins at 32 rpm when in water that is moving at 2.0 m/s. The rotational inertia of the propeller is approximately 3.0 kg∙m^2. Determine...
Homework Statement
A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius of .2 m. A 1.50 kg mass is attached to a very light wire that is wrapped around the rim of the pulley, and the system is released from rest. a) How far must the stone fall so that the...
Homework Statement [/B]
An ice skater executes a spin about a vertical axis with her feet on a frictionless ice surface. In each hand she holds a small 5kg mass of which are both 1m from the rotation axis and the angular velocity of the skater is 10rad/s. The skater then moves her arms so that...
Homework Statement
A thin stick of mass M = 2.8 kg and length L = 2.2 m is hinged at the top. A piece of clay, mass m = 0.8 kg and velocity V = 2.7 m/s hits the stick a distance x = 1.65 m from the hinge and sticks to it.
Q2: What is the ratio of the final mechanical energy to the initial...
Homework Statement
Uniform rod rotates at axel. What is the total kinetic energy of the rod?
Homework Equations
deltaKrot = 1/2Iw^2
deltaKtrans = 1/2mv^2
The Attempt at a Solution
I believe the rod has both rotational as well as translation energy because the rod is not rotating about its...
Homework Statement
Imagine a ball with moment of inertia I_{cm} = \beta MR^2 encountering a circular loop of radius R_0 > R after rolling on a level surface at a speed of v_0. Assume that the ball does not slip. Attached a diagram.
A) What is the minimum value of v_0 required for the ball...
[Moderator's note: spun off from another thread.]
How would Einstein calculate the rotational energy of a 6 kilometer long rigid bar with rest mass M rotating about its center with 15000 revolutions per second in gravity free space?
I feel like this is a very simple concept that I seem to confuse more often than I'd like to admit. Namely, if you have a rotating simple pendulum (or really any object), why does it have 0 translational kinetic energy if it is kept rotating around a fixed axis? The centre of mass is constantly...
I have a question regarding the rotational energy equation, derived based on the rigid rotor assumption:
##\epsilon = k\theta_r J (J+1)##
where k = Boltzmann constant, and J is the rotational quantum number.
The degeneracy is 2J+1.
Let's assume the constant quantity ##k\theta_r## = 1 and...
Homework Statement
So I have a horizontal pulley positioned at the edge of table with a mass of .2kg hanging down from a height of .76meters, the other end of the string is attached to a wooden block of mass .25kg that when the .2kg weight is dropped the wooden block is pulled towards the...
Hello everyone
I have a question regarding radians and the unit of rotational energy (which has been probably asked several times elsewhere but is still confusing for me :-) ).
As I understand radian (rad) is a UNIT that is dimensionless (thus cannot be omitted), correct ?
Now if I want to...
Homework Statement
Suppose that some time in the future we decide to tap the moon's rotational energy for use on earth. In additional to the astronomical data in Appendix F in the textbook, you may need to know that the moon spins on its axis once every 27.3 days. Assume that the moon is...
Homework Statement
Consider a uniform rod of mass 12 kg and length l.0 m. At its end, the rod is attached to a fixed, friction-free pivot. Initially the rod is balanced vertically above the pivot and begins to fall (from rest) as shown in the diagram. Determine,
a. the angular acceleration of...
Homework Statement
In the normal loop the loop problem involving rotational energy where the marble goes down the hill and goes through a loop the loop, it asks for the minimum height of the hill to keep the marble on the track.
Homework Equations
But why does the normal force have to equal 0...
Homework Statement
Two masses are connected by a string that hangs over a frictionless pulley with mass 8kg, radius .25m, and moment of inertia .5mr^2. One mass lays on the ground and has mass 15kg. The other mass is 22.5 kg and is 2.75 m above the ground. Use conservation of energy to...
Homework Statement
A cart whose body has mass M = 1.5 kg is set on four tires each of which has mass m = 0.3 kg and radius r = 0.1 meters. Each tire can be treated as a solid disk with rotational inertia mr2/2. The cart is set on an incline a height h = 1.2 meters high and released. At the...
Homework Statement
A frictionless pulley has the shape of a uniform solid disk of mass 5.00 kg and radius 28.0 cm . A 1.40 kg stone is attached to a very light wire that is wrapped around the rim of the pulley, and the stone is released from rest. As it falls down, the wire unwinds without...
Hi!
I got the task to determine the moment of inertia of a hollow cylinder, however it's not about just measuring the mass and the inner and outer radius and putting it into the right formula, instead I should roll it down an inclined plane.
1. Homework Statement
I'm only allowed to use the...
< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >
So the problem that I have been assigned has formulas of rotational energy, momentum, trajectories, inertia, and inclined planes. A solid sphere is rolling down an inclined plane (that is placed...
Homework Statement
So a car owner wants to change his current tires and rims to a wider set of tires and rims for increased handling ability. However, the owner does not want to lose any acceleration performance due to the increased friction of having wider tires. To combat this, the owner...
Homework Statement
The vertical exercise wheel in a mouse cage is initially at rest, but can turn without friction around a horizontal axis through the center of the wheel. The wheel has a moment of inertia I=0.0004kg m2 and radius R = 0.06m An extremely smart pet mouse of mass m = 0.03 kg runs...
Suppose I have some sort of rigid body, a solid sphere let's say. For simplicity's sake let's assume that the sphere can only rotate about a single arbitrary axis through the center of mass. If the center of mass of the sphere is traveling with a constant velocity (with respect to some arbitrary...
Homework Statement
Energy is released by the Crab Nebula at a rate of about 5×10^31W, about 105 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once...
http://www.aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf
Homework Statement
Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs.These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on...
A solid marble starts from rest and rolls without slipping on the loop-the-loop track in Fig. 10.30. Find the minimum starting height from which the marble will remain on the track through the loop. Assume the marble’s radius is small compared with R.
Solution:
In the question, why is the...
60. A ship’s anchor weighs 5000 N. Its cable passes over a roller of negligible mass and is wound around a hollow cylindrical drum of mass 380 kg and radius 1.1 m, mounted on a frictionless axle. The anchor is released and drops 16 m to the water. Use energy considerations to determine the...
Homework Statement
In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge...
Homework Statement
Figure: http://i.imgur.com/E2D1hkW.png
A massless rod of length 2R is attached at the middle to a pivot point that allows it to rotate in the vertical plane. Masses m and 2m are attached to the rod at the locations depicted in the figure. Initially the rod makes an angle of...
Hi,
I am a little confused about the energy conservation of a pin ended free falling rod.
When i try to derive energy conservation equation i am not sure including angular and linear velocity at the same time. I try to visualize the problem in the attached picture and put my derivation also...
I have solved an exercise and I'd like to know if my proceeding about finding kinetic energy is correct or not, because this is the first time that I "meet" a situation like this.
"A bar has mass M and length l. Its extremity A is hooked to a coil (with length at rest l0), its extremity B is...
Homework Statement
Hey guys I have two questions. The first one I'm not sure, while the second one, I have some idea but don't know how to proceed with answering the question.
1. A rapidly spinning flywheel has been suggested as an energy storage mechanism for cars. Let's consider a 300kg...
Homework Statement
A uniform rod of length L1 and mass M = 0.75 kg is supported by a hinge at one end and is free to rotate in the vertical plane (Figure). The rod is released from rest in the position shown. A particle of mass m = 0.5 kg is supported by a thin string of length L2 from the...
I was thinking about the rotational kinetic energy of fluids the other day and I realized that I have a huge gap in my knowledge of physics. Why doesn't rigid body rotational kinetic energy (KE = 1/2*I*ω^2) not apply to fluids or deformable bodies (it should at least be proportional to that...