2
votes
1answer
125 views

How do I convert tangential speed to angular speed in an elliptic orbit?

I am running an animation of a satellite in an elliptic orbit (defined by a parametric equation for $x$ and $y$ as a function of $t$) and want to make sure the spacecraft is traveling at the right ...
1
vote
2answers
68 views

Does an object on top of a lever arm have angular velocity at the moment when the lever is released?

Suppose there is a lever arm fixed at one end, and it is parallel to the ground. There is an object resting somewhere on top of the lever arm (the object is not attached to the lever). At the moment ...
0
votes
1answer
94 views

How do I find angular and linear velocity after normal force and “infinite” friction force?

Look at this picture: http://i.imgur.com/mY8ShkV.png Here we have a ball resting on top of a platform (the contact point is marked red). I know the normal vector (marked green). I also know the mass, ...
3
votes
1answer
99 views

Paradox of angular velocity

For a torque-free symmetric top, the Inertia tensor has an inverse $I^{-1}$, and $L=I\omega$. Which implies that $\omega=I^{-1}L$. But since $I, L$ are constants, $\vec\omega$ is a constant. However, ...
1
vote
1answer
102 views

Why is body frame angular velocity nonzero?

This question is relevant to Euler's angles and Euler's equations for a rigid body. Why aren't $\omega_1$, $\omega_2$ and $\omega_3 = 0$ in the body frame? How can we measure $\vec\omega$?
0
votes
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 ...
7
votes
2answers
390 views

Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
3
votes
1answer
973 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.
-1
votes
1answer
232 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
3
votes
1answer
106 views

Two masses on rope spinning around

Two balls of the same mass $m$ are connected to each other with rope of length $l$. One of the balls is also connected to the ceiling with a rope of the same length $l$. The balls are spinning ...
0
votes
1answer
293 views

Circular motion and centrifugal force

Assuming a race car drives around in a circle of radius r, center (0,0), linear velocity v, and ignoring centrifugal forces and friction I can calculate the position at any time, t. Angular velocity ...
0
votes
2answers
319 views

Lagrange-Euler equations for a bead moving on a ring

A bead with mass $m$ is free to glide on a ring that rotates about an axis with constant angular velocity. Form the Lagrange-Euler equations for the movement of the bead. Solution: Let us ...
5
votes
1answer
450 views

Rod slipping against block due to gravity? [closed]

A uniform rod of mass $m$ and length $l$ is pivoted at point O. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a ...
3
votes
2answers
3k views

Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am fully ...
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 ...
1
vote
2answers
877 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 ...