geogebra Tag Posts Index

Example 4: Newton's Second Law of Motion and Centripetal Force

In this video, I go over the vector version of Isaac Newton's 2nd Law of Motion, which states that if a force F acts on a particle of mass m producing an acceleration

Example 4: Newton's Second Law of Motion and Centripetal Force

In this video, I go over the vector version of Isaac Newton's 2nd Law of Motion, which states that if a force F acts on a particle of mass m producing an acceleration

Example 3: Integrating Acceleration and Velocity Vectors to get the Position Vector

In this video, I show that we can obtain the velocity of a moving object by first integrating its acceleration vector to obtain its velocity and then integrating

Example 3: Integrating Acceleration and Velocity Vectors to get the Position Vector

In this video, I show that we can obtain the velocity of a moving object by first integrating its acceleration vector to obtain its velocity and then integrating

Example 2: Velocity and Acceleration of an Object moving in 3D

In this video, I go over an example of obtaining and graphing the velocity and acceleration vectors of an object moving in 3D whose position vector is known. This

Example 2: Velocity and Acceleration of an Object moving in 3D

In this video, I go over an example of obtaining and graphing the velocity and acceleration vectors of an object moving in 3D whose position vector is known. This

Velocity and Acceleration as Derivatives of the Position Vector + Example of an Object moving in 2D

In this video, I show that the derivative of the position vector of a particle moving in 3D space is just the velocity, and likewise the acceleration is obtained

Velocity and Acceleration as Derivatives of the Position Vector + Example of an Object moving in 2D

In this video, I show that the derivative of the position vector of a particle moving in 3D space is just the velocity, and likewise the acceleration is obtained

The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix

In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. The

Normal and Binormal Vectors + Example on a Circular Helix

In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. YouTube - Summary

Arc Length of a Space Curve + Example on Circular Helix

In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral

Vector Functions: Arc Length and Curvature

In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. The arc length for a space

Example 4: Tangent Vector is Orthogonal to Vector of Constant Length

In this video I show that the tangent vector (derivative of a vector function) is orthogonal or perpendicular to a vector of constant length. Geometrically this

Example 3: Tangent Line to a Helix

In this video I show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. YouTube

Example 3: Tangent Line to a Helix

In this video I show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. I first

Example 2: Sketching the Tangent Vector

In this video I go over another example on derivatives of vector functions, and this time sketch the tangent vector to a plane curve manually as well as with GeoGebra's

Definition of Derivative for Vector Functions

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of

Definition of Derivative for Vector Functions

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of

Exercise 3: Manually Graphing the Projection of the Trefoil Knot onto the xy-Plane

In this video I manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I begin by converting the parametric

Charged Particles Moving in Electromagnetic Fields

In this video I show that space curves can be used to model charged particle motion in orthogonally oriented electric and magnetic fields. Depending on the speed