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

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1answer
302 views

Finding stopping time when only given initial angular velocity and an expression for angular acceleration?

Question: A wheel starts is spinning at $27\text{ rad/s}$ but is slowing with an angular acceleration that has a magnitude given by $\alpha(t) = (3.0\;\mathrm{rad/s^4})t^2$. It stops in a time ...
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1answer
19 views

Angular velocity vector in terms of motion of an object

May be it is small question in this forum but I'm trying to get the feel of the understanding about the angular velocity. If this question is getting rejected please kindly refer me to appropriate ...
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2answers
66 views

Rod sliding on a frictionless surface

A uniform rod$(m,l)$ is standing vertically on a horizontal frictionless surface. Gravity is downwards and uniform. I give its upper end a little push and off it goes. I want to find the Normal ...
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5answers
240 views

Does Gravity / curved space cause rotation?

Does Gravity / curved space cause rotation? Meaning, if a spaceship is heading not directly toward Earth, but slightly off to one side, and when finally being close to the Earth it falls into earth ...
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4answers
118 views

Does car have more kinetic energy when turning?

I asked this Phys.SE question Does car lose kinetic energy when turning? Assume a car turning without losing its speed by holding to a point by a rope. IMO, while the car is turning, its kinetic ...
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4answers
137 views

Does car lose kinetic energy when turning?

I am writing simple car simulation. Assume non friction, then in straight line the car doesn't lose speed. But what if the car is turning, there should be some kinetic energy loses to change the ...
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3answers
258 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
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3answers
52 views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
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1answer
54 views

Rigid body problem

I have some doubts about the next excercise: A bar of length $2a$ and mass $m$ moves freely with both of its extremes on a ring of radius $\sqrt2a$. The ring can rotate freely in a certain ...
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4answers
501 views

If a pendulum is on a rotating table, will a torque be generated?

Here is the set up. Very simple. A flat (i.e. horizontal table, there is no gravity) and rounded table that spins on its axis (through the center of the table). A spring mass system is now put on the ...
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1answer
35 views

Is there no problem in thinking of any motion of a rigid body as a composition of translational motion and rotation w.r.t center of mass?

Sometimes when I work on mechanics problems, I wonder if this analysis is always valid. Couldn't there be some motion of a rigid body that cannot be expressed as a composition of translational ...
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1answer
26 views

Kinematics with non constant acceleration II [closed]

I'm getting crazy with this problem and I think that it's pretty simple. An helicopter's helix is spinning at initial speed $w_0=200\ rpm$, all of a sudden the motor stops and it decreases its ...
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0answers
187 views

Different directions of frictional force when objects are rolling

My textbook has two instances of rolling bodies (smooth rolling). In the first, the body is rolling on the horizontal floor with some acceleration of its centre of mass. In this case, the book says ...
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0answers
134 views

Lagrange's Equations for a Tetherball

I'm trying to write down the equations of motion for a tetherball moving around a pole while the string is getting shorter. --- MAJOR EDIT --- I started with Lagrange: $$ x(t)=l(t) \sin (\theta) ...
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1answer
95 views

Could moving land mass alter Earths gravity?

This is potentially a very stupid question but I'm going to ask it anyway. With all these huge buildings such as the Abu Dhabi Mosque, where an unbelievable amount of materials such as marble was ...
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1answer
38 views

Total energy of a body following circular motion

I learned that when a body rotates, its total energy is, $$energy=\left(\frac12\right)mv^2 + \left(\frac12\right)I\omega^2 $$ However, if an astronomical object is orbiting around the earth, is ...
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8answers
4k views

Why is the moment of inertia for a hollow sphere higher than a uniform sphere?

I have completely no idea and I am inquiring about this as it is an interesting question that popped in my head while doing physics homework.
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0answers
46 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 ...
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1answer
52 views

Reaction force of the ground beyond the equator

Let's imagine a person standing somewhere on Earth, but not on the equator, i.e. somewhere with a positive net value of latitude. Since the Earth spins around its axis and the person spins along, the ...
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2answers
99 views

Differentiating a vector product

$$m_i\mathbf{r}_i\times\frac{\mathrm{d}^2\mathbf{r}_i}{\mathrm{d}t^2} = \frac{\mathrm{d}}{\mathrm{d}t}\biggl(m_i\mathbf{r}_i\times\frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t}\biggr)$$ I do not ...
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1answer
62 views

Motion of rigid body system in absense of work

In the absence of work on the system, is there a closed form equation for the motion of a set of constrained rigid bodies (let's say, using Revolute (ie: simple pivot) constraints)? If the bodies are ...
2
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1answer
71 views

Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a ...
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0answers
41 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 ...
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2answers
540 views

Where does a spinning figure skater's energy go when she slows down?

Today in physics class we were talking about angular momentum and rotational kinetic energy. My teacher used the classic example of a figure skater spinning on ice - when she pulls her arms in, her ...
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1answer
142 views

Applying multiple forces to one object and calculate net movement and rotation?

I'm working on a small game as a hobby project, and I've run into a problem that would seem simple, to me, but that I can't find any information on or solution to. How would one go about figuring ...
2
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2answers
113 views

Angular Momentum of a rigid, extended object

Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum. It is often said that an object that has been thrown up in the air ...
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2answers
107 views

If a spaceship was pulled toward a sun, would it spin?

I was watching a movie. A spaceship was forced into "warp speed". The co-ordinates could not be set. The spaceships trajectory was that of a nearby sun. Forcing the spaceship to power down was the ...
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1answer
63 views

Stability of square of masses on strings under rotation

Imagine we have a square of masses, $m$, connected by light inextensible strings, length $l$, rotating around it's centre at angular speed, $\omega$. It's easy enough to show that there must be a ...
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2answers
195 views

Relative linear velocity of a particle to a rotating object

I am trying to calculate the "relative linear velocity" of a particle moving over a rotating object. According to this paper (section 2.2) I am reading the relative linear velocity is calculated by: ...
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3answers
612 views

force applied not on the center of mass

When applying a force outside of the center of mass of the body, the body will get both linear and angular momentum. Right? Does the linear velocity from this force equal to the linear velocity from ...
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0answers
71 views

Torque in an accelerated frame of reference

I'm taking a mechanics course this year and are currently studying rotational motions for my finals. The book we have explains it mostly fine, but there is one question I can't seam to find an answer ...
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2answers
305 views

Between a solid and a hollow cylinders of the same mass, which one has the greater rotational kinetic energy?

I know that rotational kinetic energy is $\frac{1}{2}I\omega^2$. Therefore, the rotational kinetic energy will depend on the moment of inertia. I came to the conclusion that since both have the same ...
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3answers
464 views

Origins of Moment of Inertia

Where exactly does the equation $MR^2$ for moment of inertia come from? The quantity itself seems fairly arbitrary.
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1answer
86 views

Integration on a general equation for instantaneous angular acceleration

An equation for instantaneous angular acceleration is given as: $$ \alpha \equiv \lim_{\Delta t\to0}\frac{\Delta \omega}{\Delta t} = \frac{d\omega}{dt} $$ The text I am reading says writing this ...
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1answer
137 views

Ball on a slope [closed]

I have a lab report, but I can not write it in a correct way. The lab experiment was about a ball rolling on a slope, I have a height of the slope, the distance, and the time in which the ball spent ...
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2answers
168 views

Internal/Rotational angular momentum

I have some difficulties to understand the relation between the internal and the rotational angular momentum of a rigid body which is also known as K├Ânig's theorem, so what physical intuition lies ...
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1answer
120 views

Does angular momentum conservation imply that angular momentum $J$ is parallel to angular velocity $\omega$?

In other words, does $\frac{dJ}{dt} =0$ imply $J \times \omega =0$? Counterexamples or proofs would be helpful! EDIT: This question originally asked if $\frac{dJ}{dt} =0 \Leftrightarrow J \times ...
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2answers
9k views

What is the difference between angular speed and tangential speed in a circular motion?

I was looking a long time for the way the equations of this two speeds are obtained, and i found pretty much nothing important, so can someone explain how are those obtained, and which is the ...
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4answers
178 views

Rotation axis of a rigid body

I am confused about a trivial concept. Let the rotation of a rigid body, say with one point fixed, be described by the equation $\vec{x}(t)=R(t)\vec{x}(0)$, with $R(0)=I$. Then, at each instant ...
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0answers
60 views

How to check a worm and a worm gear fit? [closed]

I know the diametral pitches must match for spur gears in order for them to run together. How to check worm gear and worm? Thanks
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1answer
132 views

Expression for kinetic energy of gas per molecule

The average kinetic energy (KE) per molecule of a gas is $\frac{3}{2}kT$. While finding this we do $$ \text{ Average KE} =\frac{1}{2} M \frac{1}{N}\sum v^2=\frac{3}{2}kT$$ But why do we not add ...
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5answers
1k views

Earth moves how much under my feet when I jump?

If I'm standing at the equator, jump, and land 1 second later, the Earth does NOT move 1000mph (or .28 miles per second) relative to me, since my velocity while jumping is also 1000mph. However, ...
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1answer
178 views

If I jump will I land in the same spot? [duplicate]

If I were to jump one meter in the air and hang for one second, would I fall back down in the same spot or would the earth rotate ever so slightly under me, causing me to land a short distance away ...
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1answer
992 views

Example where angular momentum and angular velocity are not parallel

I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.
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1answer
543 views

How come a rigid body has 6 degrees of freedoms (DOFs) ? Isn't velocity a DOF?

For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?
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1answer
94 views

Landau Lifshitz energy for uniform rotation

Landau Lifshitz claim in their Mechanics book (39.11) that for a uniform rotation we have $ E = \frac{mv^2}{2} - \frac{m}{2} (\omega \times r)^2 + U,$ where the rotation is given by $v' = v + \omega ...
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3answers
543 views

What makes the Earth keep spinning?

I am thinking of what makes the Earth keep spinning? Is there anybody here know the answer?
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0answers
59 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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5answers
1k views

Veritasium - Firing bullet in block - along center and away from center

This question is about this video on YouTube, in which a bullet is fired vertically into the center of a wooden block from below, sending the block up into the air. Next, a bullet is fired vertically ...
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2answers
370 views

Extracting acceleration vector from rotated aircraft

Suppose we have an aircraft with accelerometer measuring accelerations along each axis. It is mounted in a way so it is perpendicular to the plane in all axes (that should be obvious). We also have ...