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53 votes

Is the speed of Earth's spinning constant over a given 24 hours?

The rotation of the Earth (~73 µrad/s) does speed up and slow down by a few picoradians per second during the day because of solar/lunar tidal forces acting on the asymmetric distribution of the Earth'...
David Bailey's user avatar
  • 11.5k
49 votes

How can I determine the rpm of a wheel that's spinning really fast?

There's a very interesting way to find the angular velocity of a wheel that's spinning so fast that you can't measure using a stopclock. We'll be using a strobe light (a light that flashes on and off ...
Pritt Balagopal's user avatar
40 votes

Why are angles so weird?

Your concerns are valid, and for that reason, there is also an alternative way to view angular velocities, angular momentums, etc.: They are not vectors, but bivectors. A bivector is essentially an ...
Vercassivelaunos's user avatar
30 votes

Why are angular mometum and angular velocity not necessarily parallel, but linear momentum and linear velocity are always parallel?

Note that this answer, like the tags of the question, is only focusing on Newtonian mechanics. The definition of linear momentum $\mathbf p$ is expressed in terms of the linear velocity $\mathbf v$ ...
BioPhysicist's user avatar
29 votes

How fast does Haumea rotate?

From Wikipedia, the sidereal rotation period is 3.91 hrs, so the angular frequency of its rotation is $2\pi/(3.91 \, \mathrm{hrs}) = 4.48 \times 10^{-4} \, \mathrm{rad/s}$, or $7.12 \times 10^{-5} \, \...
Sebastian's user avatar
  • 1,045
28 votes
Accepted

Can the direction of angular momentum and angular velocity differ?

Consider a thin rectangular block with width $w$, height $h$ resting along the xy plane as shown below. The mass of the block is $m$. The mass moment of inertia (tensor) of the block about point A ...
John Alexiou's user avatar
  • 38.7k
28 votes

Is Earth’s rotation slowing down or speeding up?

There are few competing processes regarding Earth's rotation. The major two are Tidal friction - Moon and Sun tides keep transferring angular momentum from the Earth's rotation into the orbital ...
fraxinus's user avatar
  • 7,916
27 votes
Accepted

Why is the velocity different for different points on a rolling wheel?

You have to remember that the entire wheel is also moving. Think of this. Where the wheel meets the ground, the velocity of the contact point must be 0, otherwise the wheel would be skidding. Another ...
hdhondt's user avatar
  • 11k
26 votes

How can I determine the rpm of a wheel that's spinning really fast?

A laser tachometer: https://www.amazon.com/Neiko-20713A-Digital-Tachometer-Non-contact/dp/B000I5LDVC Make a mark at one point on the motor, then set it spinning. Point the tachometer at it. By ...
SomeoneSomewhereSupportsMonica's user avatar
25 votes

Does cutting of trees affect spin angular momentum of earth?

Model the tree as a point mass $m$ located some height $h$ above the ground --- that is, forget the mass of the trunk and assume all the mass of the tree is in the branches and leaves above the ground....
rob's user avatar
  • 90.9k
24 votes

How can I determine the rpm of a wheel that's spinning really fast?

One idea for an approach may be to record the sound the motor produces and then Fourier transform that signal. The assumption is that the frequency you look for will be prominently visible in the ...
Gregor Michalicek's user avatar
23 votes

Why is the velocity different for different points on a rolling wheel?

In the no slipping condition the translational speed $v$ of the centre of mass of the wheel and the angular speed of rotation $\omega$ of the wheel are related. $v= r \omega$ where $r$ is the radius ...
Farcher's user avatar
  • 97.1k
23 votes

Is the speed of Earth's spinning constant over a given 24 hours?

The answer is that it depends on how technical you want to get. At first approximation, no, the speed of the Earth's rotation is constant. Getting more technical, the speed of rotation of the Earth ...
Alex Vaughan's user avatar
21 votes

How can I determine the rpm of a wheel that's spinning really fast?

Print out a disk that looks like this: Attach it to the spinning object and then observe it with a 60 Hz strobe light. By determining which rings look like they are stopped by a 60 Hz strobe you can ...
Eric Lippert's user avatar
  • 1,539
21 votes
Accepted

Why are the units of angular acceleration the same as that of angular velocity squared?

They have the same units of $\mathrm s^{-2}$ only if you don't use $\mathrm{rad}$ unit for bookkeeping (which you can indeed avoid because radians are technically dimensionless, similarly to turns and ...
Ruslan's user avatar
  • 29k
21 votes

Why are angular mometum and angular velocity not necessarily parallel, but linear momentum and linear velocity are always parallel?

The other answers that say the difference arises because there is an inertia tensor in the rotation case are all perfectly correct, but i think we can go deeper and more intuitive that this and say: ...
Selene Routley's user avatar
20 votes
Accepted

Is the right hand rule a trick to avoid tensors?

Angular momentum is most naturally a skew two-index tensor $L^{ab} = x^ap^b-x^bp^a$. Indeed, in higher dimensions, the two-index language is essential. In 3-d the $SO(3)$ invariance of the Levi-...
mike stone's user avatar
  • 53.9k
20 votes
Accepted

Cat righting reflex: Is the cat's angular speed zero or non-zero? (Or is it more complicated?)

The cat is not a solid and therefore we cannot define a single angular velocity: each point has a different angular velocity. And it can be nonzero even if the total angular momentum is zero.
Vincent Fraticelli's user avatar
19 votes
Accepted

What if the net force provided for a circular motion is larger than the required centripetal force?

Let's be more exact about this: Newton's second law for planar motion in polar coordinates is given by $$\mathbf F=m\left(\ddot r-r\dot\theta^2\right)\hat r+m\left(r\ddot\theta+2\dot r\dot\theta\right)...
BioPhysicist's user avatar
18 votes
Accepted

Understanding terms Twist and Wrench

Both twist and wrenches are screws. "Screw" is the general term, and "Twist" is the specific application to motion whereas "Wrench" is the specific application to forces ...
John Alexiou's user avatar
  • 38.7k
17 votes
Accepted

Why is angular velocity the same for all points on a spinning disk, even though they are at different radii from the center?

Because angular velocity is measured in radians per second. Every point on a spinning disk along a radial line from the centre completes one full revolution ($2\pi$ radians) in exactly the same amount ...
Charlie's user avatar
  • 6,953
16 votes
Accepted

Circular motion of two bodies: how to determine when they meet up again?

If you use Keplers third law $T^2/a^3=\textrm{const},$ you will know the relative orbital periods by knowing the relative size of the major axes of the two orbits. You can calculate $nT_1=mT_2.$ If ...
trula's user avatar
  • 6,225
15 votes
Accepted

How can the angular velocity vector be obtained from angular displacement which is not a vector?

There's two possible views here. One of these is that you can, indeed, consider angular displacement or position as a vector in that it can be encoded with one: if you have $$\mathbf{\Theta} := \left&...
The_Sympathizer's user avatar
13 votes
Accepted

Why are angular velocity and angular frequency not measured in Hertz?

The intended meaning of the hertz unit is that one hertz represents one complete occurrence of a cyclic phenomenon in one second. Angular frequency is not the number of complete rotations occurring ...
The_Sympathizer's user avatar
13 votes
Accepted

Where is the reaction force of an object that has just flung out from a circular motion?

While an object is in uniform circular motion, the force that is acting upon it is directed to the center. This force is what prevents the object moving linearly if the force suddenly vanished. If ...
joseph h's user avatar
  • 29.7k
12 votes

How can the angular velocity vector be obtained from angular displacement which is not a vector?

The key is in the parenthetical statement in your first block quote: focus on the "unless they are very small" part. This can be seen by doing the simple "experiment" below. While ...
BioPhysicist's user avatar
10 votes
Accepted

How different can the directions of angular momentum and angular velocity be?

As it happens, there are indeed limits to how different the directions of $\vec L$ and $\vec \omega$ can be. This is because the moment of inertia tensor is something called positive semidefinite, ...
Emilio Pisanty's user avatar
10 votes

How can I determine the rpm of a wheel that's spinning really fast?

I happen to have done this exact experiment over the weekend - detailed write-up below. Basically it involved a laser pointer, a photo diode, two resistors, a transistor, and an Arduino. Set the ...
Floris's user avatar
  • 119k
10 votes
Accepted

Non-constant angular velocity in orbit

Let's take this in two parts: first an exhibition of how this works for a trained physicist who has access to the tools of multivariate calculus, and second an examination of how you might explain ...
dmckee --- ex-moderator kitten's user avatar

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