50 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 ...
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31 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 $\mathbf v$ ...
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  • 53.8k
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} \, \...
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  • 1,035
28 votes
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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 ...
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  • 33.8k
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 ...
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  • 6,113
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 ...
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  • 9,854
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 ...
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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....
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  • 74.3k
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 ...
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22 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 ...
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  • 79.6k
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 ...
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  • 1,529
21 votes
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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 ...
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  • 26.6k
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: ...
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20 votes
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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-...
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  • 42.5k
19 votes
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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)...
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  • 53.8k
17 votes
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Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion

The proper derivation of the centripetal acceleration—without assuming any kinematic variables are constant—requires a solid understanding of both the stationary Cartesian unit vectors $\hat{i}$ and $\...
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  • 3,635
17 votes
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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 and momentum. All of them ...
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  • 33.8k
15 votes
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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&...
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15 votes
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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 ...
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  • 6,487
12 votes
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Intuitive explanation for why centripetal acceleration is $\frac{v^2}{r}$

Here is one simple way. A point is moving around a circle. It has a blue position vector and a red velocity vector, like this: The position vector stays the same length and rotates around and around ...
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12 votes
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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 ...
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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 ...
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  • 53.8k
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 ...
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  • 117k
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 ...
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10 votes

What actually is the vector of angular momentum?

Angular momentum has a magnitude, and is about some axis (thus has some sense of "direction). So vectors are used to represent the quantity, and much of the machinery of vectors applies to it. However,...
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9 votes
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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, ...
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9 votes

Under what conditions does the relation $\vec{L} =I \vec{\omega}$ holds good?

I am assuming that by $I$ you meant the moment of inertia relative to a given axis. Then you are right, the relation $\vec L=I\vec ω$ does not hold in general. So for example a particle in circular ...
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  • 16.5k
9 votes

Is the right hand rule a trick to avoid tensors?

Not quite an answer to the question asked, but a clarification of one of the ideas you used to build the question. As I have noted elsewhere right- (or left-)hand rules tend to appear in pairs when ...
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