A tag for questions about rotational motion, including angular velocity and angular acceleration.

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3
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1answer
180 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
2
votes
1answer
190 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and ...
2
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1answer
154 views

Why do some objects tend to change their axis of rotation while rotating?

This question struck me a few minutes back, I was at a table with a pear. It was more narrow than round.I proceeded to rotate this pear in one swift movement. It rotated for a few seconds, and ...
1
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1answer
34 views

How fast does a long object bent at the center need to be travelling in order to boomerang?

At an angle, of course. Standard pressure, average temperature, and calm wind. Bonus question: Can an object that is not bent boomerang at all? If yes, how different would the equations for this ...
1
vote
1answer
57 views

How would the angular velocity of the rod change if it slipped on the table?

I wanted to consider a second case of my homework assignment. We were asked to solve the question: A uniform rod of length b stands vertically upright on a horizontal plane in a position of unstable ...
1
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1answer
72 views

How can we find velocity, acceleration etc, of a revolving particle with respect to an observer inside the circle(not at center)

A particle is revolving in horizontal a circle of radius $R$ with constant speed of $|\vec{v}|$ and constant angular velocity $\omega$. There is another observer standing inside the circle, at a ...
1
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1answer
69 views

Angular and linear displacement of a turning car

My illustration is supposed to show a simplified car (with just two wheels, where the front wheel has been rotated $-90 \text{ degrees}$). Let the car travel at constant speed. This means that the ...
1
vote
1answer
346 views

Rotational mechanics - ball climbing a step

A wheel of radius, $R$ and weight, $W$ stands in front of a step of height, $h$ where h is less than R. What is the least horizontal force $F$ which must be applied at the axle of the wheel to allow ...
1
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1answer
166 views

How to calculate angle of inclination attained by a weigh balance on unequal loading?

Actually I need to rotate the beam (pivoted at centre) with constant angular velocity using the priciple of mass imbalance. Could anyone suggest what would be rate of decrease of mass in one pan ...
0
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1answer
25 views

For a rolling object, is the tangential velocity the same as the velocity of the center of mass?

For example, a solid disk rolling down a hill would include both rotational and linear kinetic energy. For the rotational kinetic energy ($\frac{1}{2}I\omega^2$) the angular velocity becomes $v/r$ but ...
0
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1answer
21 views

Question on relative angular acceleration

I want someone to kindly check whether I am doing (understanding) the math correctly or not. So, let's consider two bodies with constant angular velocities $\omega_1 \hat y$ and y $\omega_2 \hat x$ ...
0
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1answer
31 views

Tangencial Velocity along a circle with angular acceleration

Suppose a particle walks a circle's perimeter from 0 to pi/2. Its vertical velocity is V1, constant. Its tangential speed increases as a function of theta and V1. Given V1, r, what is the ...
0
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1answer
56 views

Speed of a point on a concentric disk setup

I have been really solving this question that my friend and I had thought of while discussing about speed of light. Imagine there is a set-up where there is a light source that is surrounded by a ...
0
votes
1answer
114 views

What is intertia tensor for tapered cylinder (solid and with separate inside and outside radii)?

I need the inertia tensor for tapered cylinders, both solid and hollow, and if possible with independent inner and outer radii on the $x$ and $y$ axes (so the cross-sections of the cylinders can be ...
0
votes
1answer
274 views

Kinematics of a differential drive robot

(I am reposting here a question I asked on stack overflow, since it actually sits right in between programming (modeling of 2D physics) and physics proper (kinematics). I think I have the physics part ...
0
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1answer
61 views

Is this movement possible?

My friend and I were arguing over some random facebook shared video. On this video, one guy throws up a rotating stick then, while it rotates on air, he kicks through it. Is it even possible? Or is it ...
5
votes
0answers
61 views

How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the SO(3) rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As showed in f.ex. this paper, ...
5
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0answers
107 views

Why does the video recorded by a falling, rotating camera seem to stabilize?

Here is a video of a GoPro falling from a plane: http://www.youtube.com/watch?v=QrxPuk0JefA Any idea what is happening when the image "stabilizes" around 0:35? I think it is because the camera's ...
4
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0answers
125 views

Alternate Formulation of Kinetic Energy for Lagrangian

So I have a question regarding this system: It is supposed to be a simple model of an aircraft with the fuselage idealized as a concentrated mass $M_0$ and the wings modeled as rigid bars carrying ...
2
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0answers
46 views

Unruh radiation in a rotating frame

Unruh radiation normally applies to linearly accelerated frames Is there an equivalent of the Unruh thermal radiation in a frame that is spinning? I am not aware of any horizon being created from a ...
2
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0answers
92 views

Why did Feynman tell “we cannot locate earth's angular position, but we can tell that it is changing”?

I was reading "Symmetry in physics" by Feynman, where he wrote: If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other ...
2
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0answers
45 views

Would a large, small mass object in orbit experience induced rotation

Imagine a large (multiple earth radii), very small-mass ring orbiting The Sun. Half of the ring would be closer to The Sun than the outer half. Since orbital velocity decreases with distance, two free ...
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0answers
62 views

Trying to understand the physical intuition on finding/deriving effective rotation radii of a rigid body

This question is inspired from the answer of this If the rolling is assumed to be without slipping, we can solve the problem by conservation of energy: $$ mg \Delta h = \frac{1}{2}mv^2 + ...
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0answers
75 views

Uranus, the Physical model to change it's rotation axle

Uranus rotates pretty wierd, it's 90-degrees tilted; Why is Uranus's axis of rotation tilted? The best answer for this is; that at a distant point in its past, Uranus was struck by a very ...
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0answers
62 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
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0answers
72 views

How Burmester's theory converts rotary motion of the crank to linear movement?

I have been studying the mechanism of Klann's Mechanical spider and there it was written that by Burmester's theory it converts rotary motion of the crank to linear movement. I tried searching but how ...
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0answers
80 views

Rotational energy with moment of inertia tensor

Some objects have a single moment of inertia value while others like ellipsoids have a tensor, if I wanted to work out the rotational energy of an oblate spheroid rotating around its z axis could I ...
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0answers
202 views

Maximum friction force for a wheel to be able to roll

The wheel with mass $M$ and radius $R$ below is free in space (it is not on the ground). A torque $\tau$ is applied to it through an engine. A horizontal force $F = \frac{\tau}{R}$ is also applied to ...
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0answers
102 views

Why does angular velocity lies in the axis passing through the center of the circumference?

I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it ...
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0answers
51 views

Calculate Rotational Intertia

If a can of soup, and a can of beans (tightly packed), are set in a race down a rough hill (has friction), the soup wins, because the inside of the can (soup) is not drawing energy from the system. ...
0
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0answers
39 views

Centripetal acceleration

I know if a particle is accelerating around the earth it has $$a= \omega*v$$ My question is how do I express this in terms of the unit vector. Would it go something like this. $$|a| = |\omega*v| $$ ...
0
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0answers
56 views

Kinetic energy of rotating rigid body

Sorry for boring you my friends. I am haunted by a problem of kinetic energy of rotating rigid body. Usually, the kinetic energy is calculated in the attached body reference. Because we could take the ...
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0answers
28 views

Does vehicle tire mass effect efficiency?

This question has an interesting origin: A tire salesman was recommending tires (aka tyres) for a highly fuel-efficient vehicle. He said the vehicle was light (compared to most production cars), and ...
0
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0answers
29 views

Relation between linear and rotational motion of molecules?

The temperature of a substance, such as an ideal gas, can be related to the root mean square speed of the molecules. For example, for gases the molecules travel at about 480 meters per second. If we ...
0
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0answers
51 views

Will future spaceships for very long distance rotate?

I have seen in the movie Interstellar and The Martian they use the model of spaceship which rotate around it's axis. This is the spaceship model from Interstellar. This is spaceship model from The ...
0
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0answers
23 views

Angular velocity in body frame to displacement in lab frame?

For the case of a freely spinning symmetric top (no gravity), I derived the following equations, where $\omega_i$ is the angular velocity about a body-fixed axis: $$ \omega_1 = w_1 \cos (w_3 t) $$ $$ ...
0
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0answers
48 views

Correct formulas for two wheeled robot motion

I'm trying to write a simulation of a two wheeled robot, which can be controlled by varying the speeds of his wheels, independently. However, the physics engine that I'm using can only rotate a body ...
0
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0answers
38 views

Find the Kinematic degrees of freedom of the following contraption

In the above mechanism it is required to find the generalized coordinates to write equation of motion of the MDOF system. I just want to ask how do we actually approach such a problem? How to ...
0
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0answers
38 views

Why do linear momentum and angular momentum have to be conserved in ground frame only?

According the Newton's second law of translational and rotational motion respectively if the net external force /torque acting on a body is zero then the linear/angluar momentum is a constant . So ...
0
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0answers
112 views

Tension in a rod rotating about a fixed point

A rod of mass $m$ and length $l$ is rising about a fixed point in the ceiling with an angular velocity $\omega$ as shown in the figure. Now, on taking a small element on the rod, the net tension ...
0
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0answers
93 views

Can a pair of members of a “rotating system” be characterized by one value of displacement magnitude?

There seems to be a claim (cmp. Goldstein, "Classical Mechanics", eq. (4-126); or also perceptable here) that values of "velocity", and of "speed", of some participant, say $P$, can not only be ...
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0answers
27 views

Power exerted by the contact force on a wheel slipping without rolling?

I was taking an old (2008) Mechanics of materials examination, and the system is a sphere on a half circular motionless rail. We first study the motion of the sphere in the case of rolling without ...
0
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0answers
31 views

Angular Speed and Normal Speed

The instantaneous speed of a point along a circular path is given by $v=\omega r$, where $\omega = \frac{\Delta \theta}{\Delta t}$, $s=\Delta \theta r$, and $v=\frac{s}{t}$. However, isn’t the ...
0
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0answers
51 views

Force acting on a wheel of a two-wheeled self balancing bot

Proceeding further with my work on a self-balancing bot as posted here: http://bit.ly/1FfI6LK I've gotten stuck at the following equation: n = Gear ratio $K_t$ = DC motor torque constant $i_l$ = DC ...
0
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0answers
110 views

Total Energy of Inverted Pendulum

I have to find the total energy $V$ of an inverted pendulum (rod). The following parameters and their values are given: Mass $m$ and length $l$ of the pendulum $\theta$ as the angle of the ...
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0answers
39 views

Problems when a disc is rotating at extreme speeds (theory)?

I was wondering the problems that would occur (aside from mechanical friction), when a disc rotates at high angular velocity. Is centripetal force an issue if high torque is applied on a disc ...
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0answers
89 views

Rotating and moving reference frame

I've looked through your forums and can't find exactly what I need. I have a two objects whos dynamics can be described in discrete time as follows: $x_A(k+1) = x_A(k) + ...
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0answers
21 views

Is it possible to impart a moment with soundwaves?

How can one adjust the properties of a sound wave to use it to spin an arbitrary object of shape S in a medium comprised of the same material. My intuition tells me that it would be much more ...
0
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0answers
80 views

Gravitational Behavior of Rotating Body

Consider a stick with a (ball-shaped) weight at the end of it. Let's say this stick is in a state of rotation (it's floating in vacuum) and is also in a state of translational motion. Consider a ...
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0answers
37 views

Need help visualising this

I was reading Irodov's mechanics (https://archive.org/details/IrodovMechanics) and when explaining rotation about a fixed axis he wrote Imagine a solid performing two elementary rotations, $d\vec ...