# Questions tagged [rotation]

Circular motion about a central point or axis

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### Is it possible to determine a final orientation from an initial angular velocity and constant angular acceleration analytically?

I am looking to model the rotation of a ball over time. I have the following information: an initial orientation, as a quaternion an initial angular velocity, as X/Y/Z components, fixed to the global ...
1 vote
54 views

### How to compute linear acceleration in 3D from change in roll, pitch and yaw angles?

We know that if a body is rotating only about $z$-axis along a circle of radius $R$ with an angular rate of $\omega$, then the acceleration of the body in 3D is $a = [0.0\ \ \omega^2R \ \ 0.0]$. Now ...
129 views

### What is meant by "rotation group"?

What do physicists mean by the term "rotation group"? Is it synonymous with $SO(3)$? Is it synonymous with $SU(2)$? I am confused because rotations in real 3D Euclidean space can also be ...
43 views

### Maximising spin on a table tennis ball: speed or acceleration?

In table tennis it is often desirable to produce as much spin on the ball as possible using a glancing contact. (The rubber covering of a table tennis bat is typically highly elastic and has a high ...
52 views

### Why do we measure plane angle in radians and solid angle in radians and steradians respectively rather than degrees? [duplicate]

Recently, I learnt about physical quantities. When i got to know about plane angle and solid angle, i had a doubt that even though they are just angles, why do we measure it in radians or steradians ...
1 vote
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### How can I optimally rotate accelerometer readings so that the integrated velocity ends up correct? [closed]

I attached an accelerometer (with gyro/magnometer) to a curling rock and threw it down the sheet of ice. The accelerometer was not flat, and it did not travel significantly in the $z$ direction. I ...
94 views

### How do we properly describe angular displacements, angular velocities, and the relationship between them (in the most general case)?

If we are merely describing rotations through a fixed axis through the origin, then it is enough to characterize angular displacements by an angle $\theta\in(-\pi, \pi]$. Real-life rotations are not ...
27 views

### How is Power Distributed in This Case?

I have been reading the working of induction motor, where I came across Torque-slip characteristics where the equation of torque was determined to be (refer figure). In the derivation the power lost ...
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### Directly get the rotation meaning of $e^{-i\frac{\theta}{2}\sigma _{\vec{n}}}$ from the commutation relation? [duplicate]

Suppose I have three hermitian operators $\sigma _x,\sigma _y,\sigma _z$ that I don't explicitly say they are Pauli matrices but still use the similar notation $\sigma_j$. They only need to satisfy ...
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### Why motional emf is induced when a one dimensional object moves?

Suppose we have a conducting rod hinged about a certain point in uniform magnetic field . When we start to rotate the rod with constant angular velocity ω, there will an induced emf of e = BωL2/2 ...
1 vote
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Consider a horizontal long rod that is undergoing free fall. Consider the torque about an axis through the rod (perpendicular to the rod and to the direction of gravitational force), that is a little ...
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### Why can the dot product of two vectors be expressed as a differential?

I am reading a book by Arfken and Weber (Mathematical methods for physicists), in the section regarding rotations in $\mathbb{R}^3$. They express the elements of a rotation matrix in Cartesian ...
1 vote
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### Unexplainable discrepancy between the centripetal force calculated directly and by linear regression

The centripetal force $F_C$ of a uniform circular motion can be expressed as, $$F_C=\frac{4\pi^2mr}{T^2}$$ where $m$ is mass, $r$ is the radius, and $T$ is the time interval for one revolution (the ...
1 vote
135 views

### Angular momentum about an axis?

We know that angular momentum of a body is defined about a point in space. Let us consider a solid cylinder whose radius is R and mass is M. It has a moment of inertia defined around the axis of ...
52 views

### Can an object have more than one axes of rotation? [duplicate]

A few answers I found say "no." Perhaps because the conditions for rotation around multiple axes have not been met. However, I have seen a couple of videos of objects spinning around both ...
151 views

### Why dimension units of radius is not $\rm m/rad$ or $\rm cm/rad$? [duplicate]

Radius is not a just simple size or length between the two points. The radius shows the connection of linear and angular values. Something must indicate the information about a perpendicularity of the ...
4k views

### Rotate an object about the time axis

Is there a notion of rotating an object about its time axis? I'm not sure if this question totally makes sense, but it seems intuitive to me that an object with dimensions in the three spatial ...
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### What is the derivative of general 3D rotation with respect to one angular component? [closed]

For a general rotation $R(t_1, t_2, t_3)$ where the $t_i$'s are the components of the rotation vector in the axis-angle representation. Is there closed formula for the derivative of $dR/dt_i$? I only ...
53 views

### Measuring the effect of spin of a tennis ball on its trajectory

Upward spin (lift) applied to a tennis ball will shorten its trajectory. Are mathematical calculations and actual experimental results on this available somewhere? If not, does anyone know how to ...
332 views

### What's the difference between spherical symmetry and rotational symmetry in quantum mechanics?

I am reading quantum mechanics and these two concepts are confusing me. Griffths' QM book says "perturbation $H'\sim p^4$ is considered "spheric symmetric", so it commutes with $L^2$ ...
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### How to find Moment of Inertia at a different axis?

So I have a solid disk: m = 2.98 kg r = 0.2 m and an axis in the - and + z direction (in unit vector form, the k dimension) And I have to find the Moment of Inertia of the disk if the axis is at point ...