Rotational kinetic energy Definition and 140 Threads
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:
E
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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:
E
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v
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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).
HELP!Rotational kinetic energy problem
Homework Statement
A 4.00kg mass and a 3.00kg mass are attached to opposite ends of a thin 42.0cm long horizontal rod. the system is rotating at angular speed omega=5.60rad/s about a vertical axle at the center of the rod. determine a) kinetic energy K...
Homework Statement
c) Three point masses lie on a rigid, rod of no mass and L = 7.71 m :
- Two particles,with the same mass m = 3.27 kg, lie on opposite ends.
- Mass M = 3.24 kg is in the center of the rod.
the rod lies along the x-axis, and rotates about the y-axis. about a point 1.68...
A 300 g ball and a 500 g ball are connected by a 60-cm-long massless rigid rod. The structure rotates about the center of the rod with angular velocity 5 rad/s. What is the rotational kinetic energy?
Attempt:
the rotational kinetic energy is given by
KEr = (1 / 2) I ω^2
where I is the...
Homework Statement
I have a motor with WK^2 = 4 lb-ft turning at 5400 RPM (3 * base speed) and I want to slow it to 1530 RPM (.85 * base speed). The motor is a 25HP 4 pole with a base speed of 1800 RPM.
How much electrical energy must I absorb?
Homework Equations
The Attempt at a...
Problem: An experimental flywheel, used to store energy and replace an automobile engine, is a solid disk of mass 200.0 kg and radius 0.40 m. (a) What is it's rotational inertia? (my calculation says 16 kg.m) (b) When driving at 22.4 m/s (50 mph), the fully energized flywheel is rotating at...
Homework Statement
What is the Kinetic Energy of the Earth Orbiting Around the Sun in Joules?
Homework Equations
E rotation = (1/2)* I * w^2
where I = moment of Inertia
where w = angular velocity
The Attempt at a Solution
Well, this is my predicament: I don't know whether...
Hello:
can someone help me with the following?
A rigid assembly of a thin hoop (of mass m and radius R of 0.15m) positioned on top of a thin radial rod (of mass m and length L = 2.0 R). (So imagine a circle on top of a stick, whereby if you extend the stick you will hit the center of the...
Homework Statement
A sphere with a 3 kg * m^2 moment of inertia about an axis through its center has its angular velocity changed by 4 rad/s owing to a 2 N*m torque applied about that axis for 6s. If its initial angular velocity is 10 rad/s, the change in its rotational kinetic energy in J...
A 30-cm diameter circular saw blade has a mass of 0.9 kg distributed uniformly in a disc.
(a) What is its rotational kinetic energy when it is operating at 4000 rpm?
(b) What average power must be applied to bring the blade from rest to its operating 4000 rpm?
Just making sure I'm doing...
Homework Statement
A 32.0 kg wheel, essentially a thin hoop with r=1.20 m is rotating at 280 rev/min. It must be brought to stop in 15.0 s. How much work must be done to stop it?
Homework Equations/The Attempt at a Solution
I=mr^2=46.08 kg*m^2
W=(1/2)I\omegaf^2 - (1/2)I\omegai^2...
Is there an amazing way I can demonstrate Rotational Kinetic Energy in a classroom? It's for a presentation and I've looked and thought about some experiments but they involve Angular Momentum which another group has to present/explain.
Sorry if this is in the wrong section, it's my first...
Homework Statement
Engineers are designing a system by which a falling mass {m} imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum ( View Figure ). There is no appreciable friction in the axle of the drum, and...
Homework Statement
The three 300 g masses in the figure are connected by massless, rigid rods to form a triangle.
What is the triangle's rotational kinetic energy if it rotates at 8.00 revolutions per s about an axis through the center?
Values given:
Mass of each ball at the corner...
[SOLVED] Rotational Kinetic Energy
Homework Statement
A solid cylinder of mass 14.0 kg rolls without slipping on a horizontal surface.
(a) At the instant its center of mass has a speed of 11.0 m/s, determine the translational kinetic energy of its center of mass.
Homework Equations...
A quote from the 'Light-dragging effects' section from wikipedia states-
"Under general relativity, the rotation of a body gives it an additional gravitational attraction due to its kinetic energy.."
Based on this, does rotational kinetic energy contribute the gravity of an object...
1.A wooden block of mass M resting on a frictionless, horizontal surface is attached to a rigid rod of length and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v hits the block and...
A bicycle has wheels of radius 0.33 m. Each wheel has a rotational inertia of 0.082 kg* m2 about its axle. The total mass of the bicycle including the wheels and the rider is 74 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the...
[SOLVED] Rotational Kinetic Energy and distribution of diatomic molecules
a) Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300 K.
b) Calculate the moment of inertia of an oxygen molecule (O2) for rotation about either the x- or y-axis shown...
Homework Statement
A solid sphere of mass 4 kg rolls w/o slipping UP an incline with an angle of 30 degrees. the radius of the sphere is 0.5 m and its moment of Inertia is I = 2/5(m)R^2. At the bottom of the incline the center of mass of the sphere has a translational speed of 5 m/s.
a)...
The marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r (see picture). What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?
This is driving me nuts. I know that the total mechanical...
Homework Statement
A bicycle has wheels of radius 0.29 m. Each wheel has a rotational inertia of 0.091 kg·m^2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle...
Homework Statement
A horizontal 813 N merry-go-round of radius 1.28 m is started from rest by a constant horizontal force of 66 N applied tangentially to the merry-go-round. The acceleration of gravity is 9.8 m/s^2. Assume it is a solid cylinder. Find the kinetic energy of the merry-go-round...
Homework Statement
A bicycle has wheels of radius 0.3 m. Each wheel has a rotational inertia of 0.08 kg* m2 about its axle. The total mass of the bicycle including the wheels and the rider is 74 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle...
Homework Statement
Suppose a solid cylindrical flywheel has a mass of 200 kg and a radius of 0.8 m and rotates at a rate of 15,000 revolutions per minute. If you were able to convert all of its rotational kinetic energy into making you run, how fast would you be going? (Assume your mass is...
how do u define rotational kinetic energy when the body is rotting about more than one axis. as an example take a ball that ia rotaing about an axis passing through the centre of ineria whiloe the centre itself rotates in an axis perpendicular to this
Hi,
on the net I found some equation, and would like to know if they are correct ones.
http://www.upei.ca/~physics/p261/projects/flywheel1/flywheel1.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/rke.html
Physics:
Stored energy = sum of kinetic energy of individual mass...
Homework Statement
A horizontal 800.0 N merry-go-round with a radius
of 1.5 m is started from rest by a constant horizontal
force of 50.0 N applied tangentially to the merry-go-
round. Find the kinetic energy of the merry-go-round
after 3.0 s. Assume it is a solid cylinder.Homework...
Hello. I'm an intro physics student, who needs help with physics problem, because my graduate student refuses to help anybody in my class anyway... here is my first question on rotational kinetic energy
1) "A uniform disk of mass M and radius R can rotate freely about a horizontal axis...
Hi there,
I am currently in the middle of studying for an exam in a few weeks time. I would appreciate it if someone could just have a quick look over the following details below and see if I am along the right lines.
1. A solid wheel of mass 15Kg is at the top of a slope 1in4. The slope...
The puck in Figure P8.51 has a mass of 0.120 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 85.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Hint: Consider the change...
A 2.4 kg cylinder (radius = 0.09 m, length = 0.50 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.74 m high and 5.0 m long. What is its rotational kinetic energy?
I just wanted to make sure that I was on the right track...
I=2/5 mr^2...
A 50kg rider on a moped of mass 75kg is traveling with a speed of 20 m/s. Each of the two wheels of the moped has a radius of 0.2m and a moment of inertia of 0.2 kg*m^2. What is the total rotational kinetic energy of teh wheels?
KEr = 1/2Iw^2
= 1/2(.02)(20)^2
= 4
Two wheels = 2...
ok, so a thread with hanging mass at the end is wrapped around a disk. the disk is dropped and mass is released. how do you find the kinetic energy of the weight at a given time/distance fallen from the disk? I'm not sure to whether use rotational kinetic energy or linear kinetic energy... all...
I have a question about this question that I hope someone can answer.
QUESTION: "A student on a piano stool rotates freely with an angular speed of 29.5rps. The student holds a 1.25 kg mass in each outstretched arm, .759m from the axis of rotation. The combined moment of Inertia of the...
Hi Please I would like to have some help with this problem:
A cylinder of mass .2 kg rolls without slipping down an inclined plane of 15 degree.
What is its rotational kinetic energy after it rolls 80cm?
I tried the formula W=Kf - Ko but It does not bring me to the solution.
Thank you for...
Please help me get this, it's due tonigh tonight on webassign. The question is:
A 3.30 m long pole is balanced vertically on its tip. It is given a tiny push. What will be the speed of the upper end of the pole just before it hits the ground? Assume the lower end does not slip.
I know to...
Hi,
I am rather perplexed by the solution to the following problem.
Particles of mass M1 and M3 are fastened to the ends of a light rod having a length l. A bead of mass M2 is free to slide along the rod between M1 and M3. Point p is the center of mass of M1 and M3, not including...
I'm afraid I need some help on this one. We are studying rotational dynamics and I read in my textbook, the explanation of a common classroom deonstration. A person sits on a rotating stool and holds heavy weights in their outstretched hands. Someone sets the individual into rotational motion...
In a crude model of a rotating diatomic molecule of chlorine (Cl2), the two Cl atoms are 2.00e-10 m apart and rotate about their center of mass with angular speed w = 1.40e12 rad/s. What is the rotational kinetic energy of one molecule of Cl2, which has a molar mass of 70.0 g/mol?
>> I...
Please, help with rotating rigid body problem
I am kind of stuck with this problem. Any takers?
A large, cylindrical roll of tissue paper of initial radius R lies on a long, horizontal surface with the outside end of the paper nailed to the surface. The roll is given a slight shove (V...