Angle between radius and acceleration

In summary, the particle is moving at a speed of 5.67 m/s and is moving in a circle with a radius of 2.50m. The acceleration vector is 15.0 m/s² and the angle between the radius and the acceleration vector is 30°.
  • #1
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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
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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 :)
 

1. What is the angle between the radius and acceleration?

The angle between the radius and acceleration, also known as the tangential angle, is the angle formed between the radius vector and the acceleration vector at a given point on a circular path. It represents the direction of the acceleration relative to the direction of motion.

2. How is the angle between the radius and acceleration calculated?

The angle between the radius and acceleration can be calculated using the formula θ = tan-1(a/r), where θ is the tangential angle, a is the magnitude of acceleration, and r is the radius of the circular path. Alternatively, it can also be calculated using the dot product of the radius and acceleration vectors.

3. What does the angle between the radius and acceleration represent?

The angle between the radius and acceleration represents the direction of the acceleration relative to the direction of motion. If the angle is 0°, the acceleration is in the same direction as the motion (tangential acceleration), while an angle of 90° indicates that the acceleration is perpendicular to the motion (centripetal acceleration).

4. Does the angle between the radius and acceleration change?

Yes, the angle between the radius and acceleration can change as the object moves along a circular path. This is because both the radius and acceleration vectors may change in magnitude and/or direction, resulting in a different tangential angle at different points along the path.

5. How does the angle between the radius and acceleration affect circular motion?

The angle between the radius and acceleration plays a crucial role in determining the nature of circular motion. If the angle is 0°, the object moves at a constant speed along a straight line, while an angle of 90° results in uniform circular motion. Any other angle results in non-uniform circular motion, where the speed and/or direction of the object changes.

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