# Angle between radius and acceleration

## Homework Statement

A particle is moving clockwise in a circle of radius 2.50m at a given instant of time.

I have to find radiant and tangential acceleration and the speed of the particle.

The acceleration vector is 15.0 m/s² and the angle between the radius and the acceleration vector is 30°

## Homework Equations

a tangential=∆v/∆t
a radial =v²/r
a =√at²+ar²
θ=?

## The Attempt at a Solution

I tried finding the acceleration components but I was not able to use the data given in a proper way. I'm sure there is an equation involving the angle but I'm not sure which one it is.
I would use θ=tan^-1( at/at) but it results in two unknowns . I'm stuck on this probably easy problem. I need someone who knows the right equations to use.
Thank you

## Answers and Replies

kuruman
Science Advisor
Homework Helper
Gold Member
Draw a picture and do a little bit of trig. If the acceleration makes an angle of 30o with the radius, what is its component along the radius? What about the tangential component which is perpendicular to the radius?

By the way, welcome to PF.

I tried finding the components of a vector using at= a sin 30 and ar=a cos 30.
ar is 12,9 m/s² and at = 7,5 m/s² . Then I found the velocity to be 5,67 m/s which looks to be approximately righ.

But what if I have the two accelerations and need to find the angle between them?

kuruman
Science Advisor
Homework Helper
Gold Member
Your numbers look correct.

Usually you are given only one acceleration which points in the direction of the net force on a system. You can have as many forces as you wish acting on an object, but its acceleration will be in one direction. An object cannot accelerate in two different directions simultaneously. Nevertheless, to answer your question, if you are given two accelerations and you have to find the angle between them, you will be given additional information that will allow you to do so. For example, the direction between the two forces that provide these accelerations may be given or implied.

Thank you very much for your reply..Actually I have given up on this exercise, but then I returned to it and forced myself (successfully ) to find an answer.

Have a good day :)