0
votes
2answers
31 views

How are the angles equal?

At the back of my mind I know they should be equal, but mathematically, how are the two $\Delta \phi$ angles equal? The only explanation present in the text is that, "both velocities are ...
1
vote
2answers
135 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 ...
1
vote
2answers
63 views

What's The Minimum distance?

My Friend gave me a question today. The question was.:: We have a point A. At a distance of $x_0$ from the point. There is a particle$(P_1)$. Also, a particle is present at the point A $(P_2)$.The ...
0
votes
1answer
39 views

From 3D velocity to coordinates

I want to calculate the 3D position $T_x, T_y, T_z$ of an object with respect to a coordinate system if I have the mean velocity (norm) $v$ and its 3D rotation $(\omega, \phi, \kappa)$ with respect to ...
0
votes
3answers
63 views

How can I compute the angular velocity of a triangle formed by three particles knowing their instantaneous positions and velocities? [closed]

I have a set of trajectories of three particles and their instantaneous velocities. I would like to compute the 3 components of the angular velocity pseudovector of the fictive triangle formed by ...
0
votes
1answer
41 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 ...
-1
votes
1answer
42 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 ...
1
vote
1answer
73 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
votes
0answers
46 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 ...
1
vote
1answer
199 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
votes
1answer
108 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 ...
0
votes
1answer
122 views

Obtaining velocity or acceleration vector of a point on a rigid body?

If I have a cube that is moving at a velocity of $v$ and spinning at an angular velocity of $\omega$, how can I determine the instantaneous velocity vector of one of the vertices of the cube? What if ...
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 ...
1
vote
1answer
532 views

Non-commutative property of rotation

Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
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 ...
0
votes
1answer
545 views

Two Different Sorts of Inertia: Inertial Mass and Moment of Inertia

There are two different sorts of inertia: inertial mass and moment of inertia. I am currently reading about moment of inertia. Now, I know inertia is an important concept; with it, we can determine ...
2
votes
1answer
316 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 ...
1
vote
1answer
447 views

Equations of motion in 2D [closed]

I'm struggling with a seemingly simple problem in 2D motion. Basically, the question is, given accelerations in $x$ and $y$ ($a_x$ and $a_y$) as well as the angular velocity ($\omega$), how can we ...
8
votes
4answers
723 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. ...