Questioning a Linear & Angular Kinematics Equation

[AJBalbirnie]

Homework Statement

I'm reviewing a chapter relating linear and angular kinematics, and I came across this equation.. why does it work and where does it come from? I can't seem to find anything in the textbook explaining it.

Homework Equations

a = sqrt( (tangential acceleration)² + (radial acceleration)² )

The Attempt at a Solution

I know all of the basics quite well, I just don't understand where this formula came from! All help will be very appreciated. Please don't go too in depth and waste your time! A simple answer should definitely suffice! Thank you! .

 

[Basic_Physics]

Pythagoras theorem: a² = ...

 

[AJBalbirnie]

Additionally, why does the square root of the two squares of acceleration equal the total. I'm not exactly sure how you would go about "Drawing a triangle" or anything like that.

 

[oli4]

Hi AJBalbirnie
The tangential acceleration and radial acceleration are orthogonal to each other. they are the components of the total acceleration.
So the triangle you are looking for is: the hypotenuse is the total acceleration and the other sides are the tangential and radial components

 

[AJBalbirnie]

Thank you. The issue is more visual to me than actually knowing the sides of the triangle though. Thanks.

 

[AJBalbirnie]

The orthogonal part makes it all go together though. Thank you.

 

[PhanthomJay]

Additionally, why does the square root of the two squares of acceleration equal the total. I'm not exactly sure how you would go about "Drawing a triangle" or anything like that.

An object or particle moving along a curved path always expeiences an acceleration directed radially inward toward the center of the curve. This is called centripetal or radial acceleration. At the same time, the particle or object may also be accelerating along the path of the curve (its circumference, if the path is circular) , which is a tangential acceleration perpendicular to the radial acceleration. Acceleration is a vector, and the total acceleration is the resultant acceleration of the two perpendicular vectors, per Pythagoras. As an example, an object moving in a horizontal circle with constant speed experiences a radial acceleration but no tangential acceleration, while an object like a roller coaster moving in a vertical circle experiences both a radial and tangential acceleration.

In the future, please post questions related to your understanding of general Physics , that are not specific homework questions, in the General Physics sub-forum.