115 votes
Accepted

Why is it possible to keep an object, say a book, horizontal while holding its corner?

Since contact forces act on the axis of rotation, they don't exert any torque. mg would exert a torque unless the book's center of gravity is directly above or below the "hinge". You are ...
AlphaLife's user avatar
  • 11.5k
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
38 votes

Is Earth really flattened at the poles because of centrifugal force?

The description from an interial frame is that the bits of the Earth at the equator are moving faster than those near the poles, so they have more kinetic energy, and thus they are a bit farther away ...
Javier's user avatar
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33 votes
Accepted

Does special relativity hold for rotating reference frames?

This has been tested, but with muons rather than apples. Muons spoil much faster than apples ($2.2\mathrm{\ \mu s}$ half life), but they don’t get squished by the enormous accelerations ($10^{18}\...
Dale's user avatar
  • 97.8k
32 votes

Spinning gyroscope loses weight?

You are substantially overstating the precision of your measurements. The readings changed rapidly so they had to be read by stepping through videos of the experiment. What you mean is that you ...
Dale's user avatar
  • 97.8k
27 votes

Acceleration without force in rotational motion?

Point 4 sounds perfectly reasonable, but it turns out to be wrong upon closer examination! Force does not require an expenditure of energy. Only force directed along the path of a moving object ...
Señor O's user avatar
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20 votes
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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

Why a moving car dips to front when brakes are applied?

Take the centre of mass as the pivot point. Weight passes through the centre of gravity, which is practically the same position as the centre of mass, and so contribute nothing to the angular ...
naturallyInconsistent's user avatar
16 votes

Is Earth really flattened at the poles because of centrifugal force?

(modified ans after corrective comment) The ground at the equator is moving fast around a circle as the Earth rotates. So there has to be a force on it, directed inwards towards the axis of rotation. ...
Andrew Steane's user avatar
16 votes
Accepted

Will spinning a bullet really fast without changing its linear velocity make it do more damage?

I believe you are right, for the following reason. The spinning bullet possesses rotational kinetic energy. If the bullet is disrupted by striking a lump of meat, that kinetic energy has to go ...
niels nielsen's user avatar
15 votes

Which Potentials lead to Kepler's second Law?

Kepler's second law is just conservation of angular momentum. Angular momentum is conserved for any spherically symmetric potential. In particular, as you note, the geometrical interpretation of the ...
Sten's user avatar
  • 4,039
14 votes

Why is it possible to keep an object, say a book, horizontal while holding its corner?

If you consider the static friction involved it is possible to achieve balance. By contrast, trying to do this with a block of ice would be almost impossible. The net squeezing forces from the top $...
John Alexiou's user avatar
13 votes

Is Earth really flattened at the poles because of centrifugal force?

Centrifugal acceleration is a real acceleration. It is an acceleration term which appears when converting Netwon's laws of motion from an inertial frame into a rotating one -- the difference between ...
Cort Ammon's user avatar
  • 46.6k
13 votes

Will spinning a bullet really fast without changing its linear velocity make it do more damage?

For comparison, the translational KE of the bullet you describe is about 2500 J while the rotational KE is about 278 J when rotating at $10^6$ rpm (assuming a 9 mm diameter and treating the bullet as ...
Michael Seifert's user avatar
13 votes

Spinning gyroscope loses weight?

One thought as to why you might see this: Is your gyroscope perfectly balanced? If not, it will generate up and down forces as it spins. At one instant, it will press down harder on the scale and be ...
mmesser314's user avatar
  • 37.7k
13 votes

Spinning gyroscope loses weight?

A lot of people have been misled by this apparent effect, notably Eric Laithwaite in his later years1. I suggest that you need to be able to collect six-axis data at the point of contact, ...
Mark Morgan Lloyd's user avatar
12 votes

Does special relativity hold for rotating reference frames?

The premise of the question doesn't really involve rotating reference frames. The circular motion of the clock or apple can be straightforwardly analyzed in an inertial lab frame. The clock moving at $...
Sten's user avatar
  • 4,039
12 votes

Does a vehicle turning on a banked road need to turn its wheels?

Introduction Your question is why we need to turn on a banked road if the normal force is already sending us around the curve. It's instructive, then, to consider what happens if there really is no ...
Charles Hudgins's user avatar
11 votes
Accepted

Why does a smooth rolling ball roll indefinitely despite there being static friction?

Real rolling objects on a horizontal plane (i.e., for $θ=0$) do not slow down due to static or dynamic friction but aerodynamic drag and rolling friction (caused by deformation of the rolling object). ...
Wrzlprmft's user avatar
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10 votes

Acceleration without force in rotational motion?

The work done by a force is the force times the distance along which the force acts. This means that it is the force times the distance traveled times the cosine of the angle between them. In constant ...
Poisson Aerohead's user avatar
10 votes

Why a moving car dips to front when brakes are applied?

The front-end dipping of the car upon braking is called dive. The torque described by naturallyinconsistent as causing dive can be managed with a front end suspension designed so the front end of the ...
niels nielsen's user avatar
9 votes
Accepted

Why are angles so weird?

Comparing cross products 3D space and 2D space is fraught with peril, at the level of your question. So, let's stick to 3D. (1) Would be a mess, and has been answered. (2) Note that: $$ \vec a \cdot \...
JEB's user avatar
  • 32.7k
9 votes

Two points of contact while rolling

It's velocity momentarily is zero. So in a time $\mathrm dt$ it'll stay where it is. This is the same kind of argument as saying that a ball thrown upwards will have a time of momentary stop, and ...
naturallyInconsistent's user avatar
8 votes

Does a vehicle turning on a banked road need to turn its wheels?

As to whether the driver needs to turn the steering wheel: there is the following extreme case: a surface banked all the way to 90 degrees. In that extreme case the wheels of the car must be pointing ...
Cleonis's user avatar
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8 votes
Accepted

When the gyro moves down, does it spin faster?

You are correct that there is more gravitational work done on A than on B in the setup that you made. The other answer is correct that the gyro is not going to spin faster just as a skateboard wheel ...
Poisson Aerohead's user avatar
7 votes
Accepted

Why is there a horizontal acceleration if there is no horizontal force?

If the floor is smooth (i.e. absolutely no friction) and horizontal then there is no horizontal force acting on the sphere and hence no horizontal acceleration. If the sphere is initially stationary ...
gandalf61's user avatar
  • 50.3k
7 votes

Why are angles so weird?

We'd like the angular velocity vector to be constant as a particle traverses its way around a circle, since a particle undergoing uniform circular motion should have uniform angular velocity. In other ...
Roger Yang's user avatar
7 votes

Does rod in free space rotate around CoM if continuous force act at one end?

The rod can be characterized by its position $\vec r = (x,y)$, which is the location of the center of mass (CoM), and its orientation $\theta$, which is the angle that the end of the rod with the ...
Dale's user avatar
  • 97.8k
7 votes

Where does this expression for infinitesimal rotations come from?

Consider a qubit system. Rotations are implemented by operators $U \in SU(2)$$^1$. The Lie group $SU(2)$ is compact and connected. Hence, the exponential map $\exp: \mathfrak{su}(2) \rightarrow SU(2)$ ...
Silly Goose's user avatar
  • 1,947
7 votes
Accepted

Are there torques affecting Earth?

Earth Rotation Variations from Hours to Centuries (Dickey) has some analysis of these variations and states that they are mainly due to interactions with the atmosphere and with the earth's core. ...
BowlOfRed's user avatar
  • 39.8k

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