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

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19
votes
8answers
6k 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
961 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?
8
votes
4answers
760 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. ...
7
votes
5answers
2k 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, ...
6
votes
1answer
163 views

Terminal velocity?

I am having a problem with a particular concept. Here is where I have gotten, since the ball never loses contact with the stair, it will rotate around through the edges, the edges being the pivot, ...
5
votes
1answer
338 views

Centrifugal force affecting satellite

I'm trying to explain the behaviour of a geostationary satellite using different frames of reference. Inertial frame: The satellite has a circular motion with angular velocity $\omega$. The ...
5
votes
1answer
1k 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
164 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
137 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
549 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
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
3answers
462 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
1answer
114 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
272 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
130 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
564 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
1answer
2k 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
385 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
2answers
232 views

So what is happening in this angular kinematics equation?

-The wheel of a car has a radius of 20 cm. It initially rotates at 120 rpm. In the next minute it makes 90 revolutions. What is the angular acceleration?_ So the answer is solved by using one of ...
3
votes
1answer
1k 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
76 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 ...
3
votes
0answers
65 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
3answers
916 views
2
votes
2answers
318 views

Proof of centripetal acceleration formula ($a_c = \frac{v^2}{r}$) for non-uniform circular motion

The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$ However, all the proofs I've seen rely on the fact that it is ...
2
votes
1answer
113 views

Why is the inertia ellipsoid of a higher symmetry than the rigid body?

I was always puzzled by this fact. A uniform cube has a sphere-shaped inertia ellipsoid. The sphere has a higher symmetry then the cube. Is there any deep reason or implication behind it?
2
votes
2answers
516 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
1answer
62 views

Why does this model fall apart when angular velocity is small?

I'm doing a physics problem in which a marble spins around a spinning bowl and both have angular velocity $\omega$. It rotates with radius $r$ around the central axis and the hemispherical bowl has ...
2
votes
2answers
1k 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
1k 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
4answers
237 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
573 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
2answers
49 views

Non-constant angular velocity

In this paper about Backstepping controll of a quadrotor helicopter an algorithm for control is described, but I have hit a dead end. In equation 15 it is described the part of state space for the ...
2
votes
1answer
86 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
141 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
3answers
86 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
1answer
613 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
501 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
328 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
4k 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
2answers
46 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
2
votes
0answers
33 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 ...
2
votes
0answers
160 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
53 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
132 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
292 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
104 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 ...