Uniform Circular Motion of an object

In summary, the problem involves a 2.0kg object rotating on a horizontal plane with a radius of 0.9m and a horizontal force of 210N exerted on it. The relevant equations are v=2\Pir/T and ar=v^2/r. By using Newton's Second Law, F = ma, and the equation for radial acceleration, the speed of the object can be calculated as v=sqrtFr/m, resulting in a speed of 9.7 m/s^2.
  • #1
brutalmadness
16
0

Homework Statement


A horizontal force of 210N is exerted on a 2.0kg object as it rotates uniformly on a horizontal plane with a radius of 0.9m. Calculate the speed of the object.


Homework Equations


I THINK the relevant equations for this problem are v=2[tex]\Pi[/tex]r/T and ar=v^2/r.


The Attempt at a Solution


v=2[tex]\pi[/tex]0.9/?
ar=?/0.9

My biggest problem is that for the life of me, I can't figure out how to find either the T or the v. If I knew how to do that, I could figure out the problem. I've also drawn a diagram of the problem.
 
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  • #2
You won't need to find T. Use your equation for "ar" as you suggest, but remember Newton's Second Law... F = ma. Since you know the Force, v can be calculated. No T needed, but if you are curious, T can be calculated now that you know v!
 
  • #3
brutalmadness said:

Homework Statement


A horizontal force of 210N is exerted on a 2.0kg object as it rotates uniformly on a horizontal plane with a radius of 0.9m. Calculate the speed of the object.


Homework Equations


I THINK the relevant equations for this problem are v=2[tex]\Pi[/tex]r/T and ar=v^2/r.


The Attempt at a Solution


v=2[tex]\pi[/tex]0.9/?
ar=?/0.9

My biggest problem is that for the life of me, I can't figure out how to find either the T or the v. If I knew how to do that, I could figure out the problem. I've also drawn a diagram of the problem.
All you need to know is that the radial acceleration (or centripetal acceleration ) is v^2/r, as you have noted. Then use Newton's 2nd law in the radial (centripetal) direction to calculate v, the tangential speed .
 
  • #4
In this case, would my F=m(a) be 2.0(210)?

I'm thinking I need to find "a" first... perhaps a=Fnet/m?
 
Last edited:
  • #5
brutalmadness said:
In this case, would my F=m(a) be 2.0(210)?

No...F = 210, m = 2.0, a is given by the equation you have stated...v^2/r
 
  • #6
Hmmm...

F=ma and a=v^2/r... F=m(v^2/r)

v^2/r=F/m

v^2=Fr/m

v=sqrtFr/m

v=sqrt 210(.9)/2.0

v= 9.7 m/s^2
 
  • #7
Right!
 
  • #8
thank you guys so much :D
 

Related to Uniform Circular Motion of an object

1. What is uniform circular motion?

Uniform circular motion is the movement of an object in a circular path at a constant speed. This means that the object's velocity is constant in magnitude and direction, but its acceleration is changing as it constantly changes direction.

2. What causes an object to undergo uniform circular motion?

An object undergoes uniform circular motion when a centripetal force acts on it, pulling it towards the center of the circular path. This force is necessary to constantly change the direction of the object's velocity and keep it in circular motion.

3. How is the speed of an object in uniform circular motion related to its radius?

The speed of an object in uniform circular motion is directly proportional to its radius. This means that as the radius of the circular path increases, the speed of the object also increases. This relationship can be described by the equation v = ωr, where v is the linear speed, ω is the angular velocity, and r is the radius.

4. Is the acceleration of an object in uniform circular motion constant?

No, the acceleration of an object in uniform circular motion is not constant. While the object's speed may be constant, its acceleration is constantly changing as it changes direction. The direction of the acceleration is always towards the center of the circular path, and its magnitude can be calculated using the equation a = v^2/r, where a is the centripetal acceleration, v is the linear speed, and r is the radius.

5. Can an object in uniform circular motion have a zero acceleration?

No, an object in uniform circular motion cannot have a zero acceleration. As mentioned earlier, the acceleration of an object in this type of motion is always directed towards the center of the circular path. If the acceleration were to become zero, the object would no longer be in circular motion and would instead move in a straight line at a constant speed.

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