Exponentiating matrices, and the kinds of linear differential equations this solves.

A quick explanation of e^(pi i) in terms of motion and differential equations

A quick explanation of e^(pi i) in terms of motion and differential equations

This content introduces a physics problem concerning the time-dependent position vector of an electron. It explains that the given vector equation, r=3Ti−4T2j+2k, allows for the calculation of the electron's position in 3D space at any...

This content provides a step-by-step solution for calculating the torque on a particle about the origin, given its position vector and an applied force vector, using unit-vector notation. It then demonstrates how to find the angle...

This content defines angular momentum (ℓ) for a particle as the cross product of its position vector (r) and linear momentum (p), i.e., ℓ=r×p=m(r×v). It clarifies that angular momentum is a vector quantity defined with respect to a...

This is the fourth video on the equations of lines and planes video series. In this video we will go over five intermediate examples that make use of the vector, parametric and symmetric equation of a line in space. An example involving...

This is the first video on the equations of lines and planes video series. In this video we will introduce vector-valued functions also known as vector functions, and go over the basics, focusing on notation and how they can be used to...

Angular Momentum as the cross product is demonstrated and derived. This is an AP Physics C: Mechanics topic.
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0:00 Newton’s Sec
ond Law Review
0:4
5 The Demonstration

1:05 The...

Circular Motion proof

This video goes over 3 torque examples. This video also ends the cross product series.

Calculus based review of the cross product torque equation, how to do a unit vector cross product problem, rotational equilibrium, the rotational form of Newton’s second law, the angular momentum of a particle and of a rigid object with...

Position is a vector that describes where a point is. The point is described by 3 orthogonal distances from a fixed axis: x, y and z. The position vector is denoted as *R*<b<br/>r/>

Unit vectors and the derivative are used to determine the velocity and acceleration of an object from the object’s r position vector. The motion is identified as Uniformly Accelerated Motion.

Vector components are reviewed. Unit vectors are introduced and an example is walked through. The “r” position vector is introduced and an example using both “r” position vector and unit vectors is worked through.

Calculus is used to derive the angular frequency and period equations for a physical pendulum. A physical pendulum is also demonstrated and real world calculations are performed. This is an AP Physics C: Mechanics...

The equations for NON rotating reference axes are:

Va = Vb + Va/b
and
a_a = a

_b + a_a/b

But these equations are only true if the relative axes are not rotating. If the relative frame of reference xy is...

Work as the dot product is defined. The dot product using unit vectors is reviewed. Several examples are worked through. Want Lecture Notes?f='http://www.flippingphysics.com/work-d...' target='_blank' rel='nofollow'>Notes?​ This is...

Here I derive the most generic equations of motion (position, velocity & acceleration) for a continuous curve. The calculus is pretty involved so I definitely recommend you hit up your math textbook first!

Calculating the moment of a force can be quite tricky (especially in 3 dimensions). A good way to solve these problems is to use the cross product noting that *M* = *r* x *F*

This is an introduction to relative velocity. There is an animation at the end which helps highlight that the motion of a rigid body can be split into both rotational and translational movement. I also show (informally) that the velocity...

Relative position summary

It explains how to find the shortest distance between two given lines in space.

For a system of particles in translational motion, we determine the position, velocity, acceleration, linear momentum, and net force.
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0:00 x, y,
and z position r/>1:32 r posi
tion
5:50...