What is rotational speed: Definition and 51 Discussions
Rotational frequency (also known as rotational speed or rate of rotation) of an object rotating around an axis is the frequency of rotation of the object. Its unit is revolution per minute (rpm), cycle per second (cps), etc.The symbol for rotational frequency is
ν
{\displaystyle \nu }
(the Greek lowercase letter nu).
Tangential speed v, rotational frequency
ν
{\displaystyle \nu }
, and radial distance r, are related by the following equation:
v
=
2
π
r
ν
{\displaystyle v=2\pi r\nu }
v
=
r
ω
{\displaystyle v=r\omega }
An algebraic rearrangement of this equation allows us to solve for rotational frequency:
ν
=
v
/
2
π
r
{\displaystyle \nu =v/2\pi r}
ω
=
v
/
r
{\displaystyle \omega =v/r}
Thus, the tangential speed will be directly proportional to r when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand. The direct proportionality of v to r is not valid for the planets, because the planets have different rotational frequencies.
Rotational frequency can measure, for example, how fast a motor is running. Rotational speed is sometimes used to mean angular frequency rather than the quantity defined in this article. Angular frequency gives the change in angle per time unit, which is given with the unit radian per second in the SI system. Since 2π radians or 360 degrees correspond to a cycle, we can convert angular frequency to rotational frequency by
ν
=
ω
/
2
π
,
{\displaystyle \nu =\omega /2\pi ,}
where
ν
{\displaystyle \nu \,}
is rotational frequency, with unit cycles per second
ω
{\displaystyle \omega \,}
is angular frequency, with unit radian per second or degree per secondFor example, a stepper motor might turn exactly one complete revolution each second.
Its angular frequency is 360 degrees per second (360°/s), or 2π radians per second (2π rad/s), while the rotational frequency is 60 rpm.
Rotational frequency is not to be confused with tangential speed, despite some relation between the two concepts. Imagine a merry-go-round with a constant rate of rotation. No matter how close or far you stand from the axis of rotation, your rotational frequency will remain constant. However, your tangential speed does not remain constant. If you stand two meters from the axis of rotation, your tangential speed will be double the amount if you were standing only one meter from the axis of rotation.
Question: Why does the oscilloscope double almost the exact value of rotational speed measured by Tachometer?
Rotational speed from Tachometer = 1930 [RPM]
Frequency of 1 period = 64.3 [Hz] which means 3857.91 [RPM]
The output waveform of hall-effect sensor is attached.
Can you have any...
I understand that it is a system with two degrees of freedom. And I chose as generalized coordinates the two angles shown in the pic I posted. I am having troubles in finding the kinetic energy of this system, cause the book tells me that the kinetic energy is something different then what I...
**My Attempt:** Here, I considered for 2 kg mass the resultant motion is zero, which means it's acceleration (a) would be zero. So, if we consider the Tension force from the 1.5 kg mass to keep 2 kg mass from falling is L, then 2×9.8-L=ma=2× 0 ⇒ L=19.6 N. But where does the tension force from...
Hi,
I am working on a project that would insert a generator/expander system to a pressurized stream of gas in order to generate electricity.
I would like to control the rotational speed of the generator in order to adjust the gas stream flow rate.
Would it be possible to control the...
Hi everyone,
The equation is one we have been given to calculate the rotational speed of the sun for different latitudes. phi = average latitude. This shouldn't be a problem for me, but for some reason I just can't trust my error calcs.
We are given :
A = 14.713 ± 0.0491◦/d B = −2.396 ±...
Homework Statement
For the pictured block and tackle system, formulate an equation to solve for the rotational speed of each sheave wheel for a given line pull speed. (ignore friction, slippage, line stretch) (Mass, force, efficiency, mechanical advantage are not the focus of this. Pulley...
Is it possible to position enough locations around the globe, that rocket thrust on the proper tangential direction might fire simultaneously and cause the Earths rotational speed to increase by some small amount ?
What considerations would need to be contemplated as to how this would impact...
Homework Statement
A dart of inertia md is fired such that it strikes with speed vd, embedding its tip in the rim of a target that is a uniform disk of inertia mt and radius Rt. The target is initially rotating clockwise in the view shown in (Figure 1) , with rotational speed ω about an axis...
I'm planning on carrying out an investigation with a golf ball and projectiles. Is there any type of equipment/sensor that I can used to measure the rotational speed/angular velocity? I know a gun chronograph can be used to detect the velocity but what can I used to detect the angular velocity...
Homework Statement
A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 6.03 rad/s. Her moment of inertia about this axis is 16.1 kg·m2. A short time later the aerialist is in the straight position, as...
In what way does mechanical efficiency in gears affect output torque and angular velocity? Mechanical efficiency affects power which is the product of torque and angular velocity. Let's say we have a gearbox with a mechanical efficiency of 0.95, hence the output power is 95% of the input power...
Hey there folks,
As a forward: I'm trying to build a "high fantasy" universe in which to write stories, but within its historical timeline of events there are some cosmological happenings that I'd prefer to not just wave a wand at, so to speak. I'd like there to be at least SOME solid...
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From what I understand as the rotor yaws, there are gyroscopic forces that act upon it and the magnitude of these depends on the speed of yawing (e.g. 10 degrees per second). What happens to the rotor rotational speed during yawing? Does it slow down? Is the aim to slow down the rotor...
Hi All,
Assume we have a package that we want it in an orbit with highest possible speed. In which orbit (low,mid,high) the package will rotate faster ? Due to smaller distance, low Earth orbit should allow more speed but there is also more air friction there. What would be the mathematical...
Hello
I'm a student and I have project making a harvesting tool which need barrel cam
I need force to cut trunk of coconut tree (I don't know it in english, what I mean is the hard part of coconut leaf)
I'm a bit confuse here
from Robert L Norton book Cam Design and Manufacturing...
Hello everyone!
This is probably the stupidest question that I've come up with, and I'm a little embarrassed asking it, but here goes:
Is it only the tangential speed that is zero of a point at the axis of rotation in a rotating solid? If not, then I don't understand how the rotational...
From wikipedia:
Rotating black hole
So, the black holes have got the upper limit for rotating? Could somebody explain me why? I can understand one reason: due to special theory of relativity the event’s horizon’s circular/linear speed cannot be more than speed of light, right? Or maybe there...
so according to wiki: protons have a Lorentz factor of about 7,500 and move at about 0.999999991 c, or about 3 metres per second slower than the speed of light (c)
If we consider speed of Earth's rotation or speed at which two galaxies approach each other (collision or otherwise)?
Hello!
How do I calculate the maximum possible rotational speed of a thin walled hollow cylinder? In other words, at what rotational speed will it explode due to centripetal force?
This picture shows the plane of rotation...
Hi,
I would like to know if it's possible to turn a cylinder full of gas (air for example) at W rd/s for have more density up ? The first drawing show the basic system turn around the center. The second drawing show the density of gas like I think it can be, black=more density, white=less...
Homework Statement
Suppose that there is a beam of neutrons with a range of wavelengths. One intends to produce neutrons of single wavelength by the use of neutron mechanical velocity selector.
The question is, if the slot in the disk B (second disk) of the selector lags the slot in the disk...
This is for self-study.
Homework Statement
The armature of a motor has 97 turns each of area 190 cm² and rotates in a uniform magnetic field of 0.33 T. A potential difference of 24 V is applied. If no load is attached and friction is neglected, find the rotational speed at equilibrium...
And if so, what is the limit?
Some pulsars spin very fast. more than 700 times per second, or even faster?
So the centrifugal force would be very strong at the equator, threatening to rip them apart.
Is there a limit on how fast a pulsar can spin before the centrifugal force would...
Rotational Speed of Car tyre?
hey guys i was trying to figure out this rotational speed of car tyre?...i have with me the diameter of the car tyre and the distance which it is traveling and the length of the car...so can anyone help? i need to find out how much times will the tyre spin and at...
Homework Statement
A NASA astronaut is placed in a rotating machine to see how well their bodies withstand G Force.
What rotational speed is needed in a device that has a 6.25 m radius to allow a 75.8 kg astronaut to experience a force that is twice his normal weight (or 2g)?Homework Equations...
Hey I'm making some kind of simulation... (in game maker) Ball collisions, ball to wall(friction)etc.
So I'm asking: how do i calculate rotational speed if i know r, mass, and distance to where is force being applyed?
I know that moment of inertia for a ball is 2/3*m*r2 and have no idea...
Homework Statement
There is a record spinning when a blob of putty falls vertically on its edge; which is .10m from the center. What is the rotational speed of the record after the blob sticks on it?
additional information:
mass of blob = .040kg
mass of record = .10kg
rotational inertia of...
I have 2 advantages of using rotational and orbital velocity of Earth in assisting easier rocket travel...
1. Uses less fuel as the rotational speed contributes to the rocket
2. Assists the rocket to easily produce the necessary escape velocity
Are there anymore adv? I can't seem to...
Homework Statement
The output voltage of an a.c. generator is
\emph{V}=\emph{NBA}\omegasin(\omegat).
When the voltage is connected across an inductor, the rms current in the inductor is found to be 10mA. What will Be the rms current if the rotating speed of the coil inside the generator is...
Hi,
I'm currently working on a project for a braking system of a carousel. Basically in order to start designing the brake I need to know what the maximum rotational speed of the carousel should be. The max diameter of the surface will be 2 meters and the maximum speed at the periphery should...
Homework Statement
Tire with a radius of 40cm spinning at 2500 rev/min. What is the rotational speed?
Homework Equations
w=v/r
w=2500revmin/40cm
w=62.5 rad/sec
Does that sound right? I am confused
Homework Statement
Space Station
A space station has the form of a hoop of radius R, with mass M. Initially its center of mass is not moving, but it is spinning with angular speed ω0. Then a small package of mass m is thrown by a spring-loaded gun toward a nearby spacecraft as shown; the...
what is the rotational speed of the hand on a clock that measures the minutes?
what is the rotational speed of the hand on a clock that measures the seconds?
I was hoping to discover how the current rotational speed of the Earth differs from the past. I'm also curious about the moon's relative distance and orbital speed in the past. And can anyone tell me how fast I am currently moving through space, given all of the variables involved.
Hi there.
I need some help with this I have confused myself ... I am trying to determin the rotational spped of our solar nebula as it would have been at r=40 000 AU. I have the facts that at 40 AU v=5km/second. what I am not sure on is do I use L=m*v*r? if so do I use the mass of the sun...
Homework Statement
A casino roulette wheel is set spinning with an initial angular speed of 15 rad/s. The ball is set spinning in the opposite direction with a constant angular speed of 20 rad/s as the
"00" passed by. If friction makes the wheel slow down with an angular acceleration of...
A casino roulette wheel is set spinning with an initial angular speed of 15 rad/s. The ball is set spinning in the opposite direction with a constant angular speed of 20 rad/s as the
"00" passed by. If friction makes the wheel slow down with an angular acceleration of 5 rad/s^2, How many...
A steel rotor disk which is part of a turbine assembly has a uniform thickness of 50mm, an outside diameter of 650mm and an inside diameter of 100mm. If there are 250 blades, each of mass 0.16 kg pitched evenly around the periphery of the disk at an effective radius of 350mm, determine the...
Homework Statement
As you approach the I-90 exit in your uncle's little red sports car convertible, you happen to notice a cat crossing the road. Not that you have any particular love of cats (especially this one, whose snooty disposition seems to beckon for a game of chicken), but you swerve...
Homework Statement
It all on the picture provided.
Homework Equations
F=ma
Fg=6.67e-11((m1m2)/r^2)
Other like basic rotational things not sure if i need them.
The Attempt at a Solution
All on the pic provided.
(WARNING TO DIAL-UPPERS) this is a link to a really larger...
If a wheel is turning at 3.0 rads/s, the time it takes to complete one revolution is about:
3.0 rads/s X 1 revolution/6.28 rads = .477 revolutions/s
now do I just times by 60s to cancel the seconds out to get 1 revolution.
The rotational speed of the minute hand of a watch is:
w=...
Wheel A of radius ra = 14.6 cm is coupled by belt B to wheel C of radius rc = 28.8 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 7.1 rad/s2. At what time will wheel C reach a rotational speed of 240.7 rev/min, assuming the belt does not slip?
I did...
1) The Earth rotates once per day about its axis. Where on the Earth's surface should you stand in order to have the smallest possible tangential speed?
would it be on the top of axis since it will not move?
2) It is possible, but not very practical, to build a clock in which the tips of the...
I found the following posted in another forum:
He did not cite the source.
He suggests that this is related to Relativity. I'm no relativity expert but I doubt the authenticity of his claims, especially the part that the rotation of a planet affects its gravitational pull. What do you think?
"The mass of the Earth is about 6x10^24 kg and its radius is about 6x10^6 meters. Suppose you build a runway along the equator, line-up a million F-16's, bolt them down, and have them all fire their engines (eastward) simultaneously for 1/2 hour. Estimate the effect that would have on the...
i have a rotating disc. I have a tachometer and a sensor tape. Where should
i stick the tape to measure the rpm correctly? How tachometer works?
One more question.
a rotating disc has kinetic energy. Why we study energy of a rotating.
Now if i stop the rotating disc according to law of...
An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has...
I want to measure the rotational speed of Io using a spectrograph, using the doppler formula. Since it is rotating around Jupiter, i have to take the velocity relative to jupiter, but I wonder tough how this is possible when Io is not rotating at an right angle to my observation point. Is there...