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

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19
votes
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.
13
votes
3answers
800 views

Do mankind and manmade activities/constructions have any effect on the rotation of the Earth?

We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples ...
8
votes
5answers
2k views

How is it that angular velocities are vectors, while rotations aren't?

Does anyone have an intuitive explanation of why this is the case?
7
votes
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, ...
7
votes
4answers
581 views

Why does a ping pong ball change direction when I spin it on a table?

When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. ...
5
votes
1answer
878 views

In tennis, why does topspin serve bounce higher than flat serve?

When receiving servers (while playing tennis), I've noticed that the tennis ball seems to bounce up higher on me when the server uses a topspin serve than when the server hits a flat serve. Why is ...
5
votes
1answer
158 views

Creating a fair 3 sided coin

I want to make a cylindrical three sided fair coin, with sides: heads, tails, and edge. What should the area of the edge be in relation to the area of the head of the coin? Assume it is all made of ...
4
votes
4answers
113 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 ...
4
votes
4answers
499 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 ...
4
votes
3answers
395 views

Do rotating bodies emit gravitational waves?

Suppose we have a cylinder of mass $m$, radius $R$ and height $h$ in rotation with speed $\omega$ around its symmetry axis with no friction (ideal situation). I'd expect this cylinder to emit ...
4
votes
4answers
2k views

Two axes for rotational motion

I understand that angular momentum is a vector, etc.. But, what really happens when some object, say a ball for example, is set to rotate along two axes? What would the resulting motion look like?
4
votes
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 ...
4
votes
5answers
237 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 ...
4
votes
1answer
126 views

Rotation of Spacetime => Change in orbit/path

Along the idea of frame-dragging; Will the rotation of a black hole, which has some velocity v and angular momentum, influence its path in 3D space? I've seen the fact that depending on the ...
3
votes
3answers
456 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.
3
votes
3answers
541 views

What makes the Earth keep spinning?

I am thinking of what makes the Earth keep spinning? Is there anybody here know the answer?
3
votes
1answer
1k views

Why is the velocity on the top of a wheel twice the velocity of its axle?

When a wheel is rolling, not skidding, and its axle moves at velocity $\vec{v}$, then a point on the top of its circumference will move at velocity $2\vec{v}$, shown below. I really don't ...
3
votes
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 ...
3
votes
1answer
355 views

Definition of angular velocity

I'm trying to follow the Feynman lectures and I'm stuck on a particular piece. Let me frame it for you before I ask my question. Nobody does it better than the author himself, we must find out how ...
3
votes
1answer
961 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.
3
votes
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 ...
2
votes
2answers
413 views

Piston movements in four stroke cycle?

I was reading about a four stroke cycle. Here's what I understood: In the first stroke, the piston starts at the top and moves down. In the second stroke, the piston moves upwards. In the third ...
2
votes
2answers
963 views

3D: Get linear velocity from position and angular velocity

I want to find out the linear velocity of a point in 3D space, (Euclidean), given: Its position Its angular velocity The point it's rotating around (fulcrum) (This is a problem I need to solve ...
2
votes
3answers
1k views

Angular momentum equations

I do not understand this because angular momentum is $L=I\omega$ ($I$ is moment of inertia;$\omega$ is angular velocity) but it I have also seen equations where $L= rmv\sin(x)$. I do not understand ...
2
votes
1answer
2k views

Merry go round physics problem?

So I have the following statement. "A merry-go-round is spinning with a fixed angular speed. As a person is walking towards the edge, the force of static friction must increase in order for the ...
2
votes
2answers
509 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 ...
2
votes
1answer
540 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?
2
votes
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 ...
2
votes
2answers
111 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 ...
2
votes
4answers
176 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 ...
2
votes
1answer
477 views

How does weight/mass affect angular momentum?

How does weight/mass affect angular momentum? For my 8th gr science fair project I have to do an experiment on angular momentum. My problem is that we have not been taught any of that in physics yet, ...
2
votes
1answer
441 views

Euler angle: space-fixed vs body-fixed axes

I am sooo confused!! Between active and passive, intrinsic and extrinsic, vectors and basis .... Stipulate that we stick to active rotations only. Then Standard derivation of $R(\alpha, ...
2
votes
1answer
292 views

Relating angular and linear kinematics

In my physics book "University Physics", there is a chapter on relating linear and angular kinematics. I understand the parts where it shows $v = r\omega$ and $a_{\text{tan}} = r\alpha$. However in ...
2
votes
1answer
3k views

What's the right way to calculate the principal moment of inertia?

I am writing a program that incorporates calculating the principal moment of inertia for a protein residue based on its component atom XYZ coordinates. I am exceedingly confused about which formulas ...
2
votes
3answers
49 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). ...
2
votes
0answers
132 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) ...
2
votes
0answers
45 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 ...
2
votes
0answers
40 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
85 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 ...
2
votes
1answer
274 views

Paradox of the Relativistic Record Player [duplicate]

Possible Duplicate: Invariant spacetime - distance - Circular Motion This is a question that I thought up a few years ago when I was taking mechanics. I asked the professor but didn't ...
1
vote
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 ...
1
vote
5answers
584 views

Why can mass not be considered concentrated at CM (center of mass) for rotational motion?

Could anyone explain the following expression: Why can mass not be considered concentrated at CM (center of mass) for rotational motion?
1
vote
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 ...
1
vote
2answers
188 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: ...
1
vote
2answers
1k views

Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
1
vote
1answer
128 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 ...
1
vote
1answer
74 views

Determine the velocity and acceleration of the vertex $B$

1) The bent rod $ABCD$ rotates about the line $AD$ whit a constant angular velocity of $90 rad / s$. Determine the velocity and acceleration of the vertex $B$ when the rod is in the position shown in ...
1
vote
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 König's theorem, so what physical intuition lies ...
1
vote
2answers
368 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 ...
1
vote
2answers
875 views

What are the expressions for rotational and translational kinetic energies of a system of point particles?

Consider a system of point particles , where the mass of particle $i$ is $\mu_i$ and its position vector is $r_i$. What are the expressions for translational kinetic energy and rotational kinetic ...