# Tagged Questions

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### What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?

Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
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### Average Velocity of a body moving in a circle with constant speed $v$ [closed]

A Body is moving with constant speed $v$ along a circle of radius $R$. Find the average velocity of the body from time $t = 0$ to $t= \frac{R}{3V}$. My attempt at the question: Let distance ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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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### 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 ...
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### 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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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...