Tangential and Normal Components of Acceleration as Derivatives of Position Vector + Example

Tangential and Normal Components of Acceleration as Derivatives of Position Vector + Example

From mes 3Speak Podcast by Math Easy Solutions

May 7, 2026

About this episode

This episode discusses the tangential and normal components of acceleration in relation to the position vector and its derivatives, including an example of a moving particle.

https://3speak.tv/watch?v=mes/e0b98544 In this video, I rewrite our earlier equations for the tangential and normal components of acceleration to be in terms of the position vector and its derivatives. This simplifies and standardizes the components of acceleration and involves the dot product for the tangential acceleration and the cross product for the normal acceleration. Interestingly, the acceleration vector always lies on the osculating plane because it has no binormal component. The normal acceleration increases by a factor of velocity squared so that doubling the velocity multiplies the normal acceleration by 4 when along a curved path. I also go over an example of a moving particle to show how to obtain the components of acceleration in a straightforward way. #math #vectors #calculus #physics #education Timestamps: Acceleration vector as tangential and normal components – 0:00 Acceleration vector is always in the osculating plane (contains both tangent and normal vectors) – 1:00 Normal component experiences greater acceleration in curved paths than does the tangential component – 3:29 Take dot product of velocity and acceleration to try to get acceleration in terms of…

People in this episode

Host: Math Easy Solutions

Topics covered

  • acceleration
  • position vector
  • tangential components
  • normal components
  • curved paths
  • calculus
  • physics

Keywords

  • acceleration
  • tangential acceleration
  • normal acceleration
  • position vector
  • curvature
  • dot product
  • cross product
  • osculating plane
  • velocity

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