Uniform circular motion proportionality question

In summary, when David doubles the length of the sling, the period of rotation will increase by a factor of √2, and when he halves the length, the period will decrease by a factor of √2. This can be derived by solving for T in the formula ac = (4π^2r) / T^2 and using the fact that the period is directly proportional to the length.
  • #1
Sean1218
86
0

Homework Statement



David spins a sling in a horizontal circle above his head. What would happen to the period of rotation if he applied the same force and the length was a) doubled, b) halved

Homework Equations



ac = (4π2r) / T2

The Attempt at a Solution



Just not sure what to do in general, I tried a few different things like this:

r [tex]\alpha[/tex] T2

2r [tex]\alpha[/tex] T2
r [tex]\alpha[/tex] T2/2

Then compared T2 and T2/2
square rooted both of them

T and T/sqrt(2)

1/sqrt(2) is 0.7, which is the answer to b), even though I was trying to do a).

edit: think I figured it out

I can just equate T and T/sqrt(2) can't I? The first T is Ta, the second is Tb, and that equation is saying that Ta is .7x smaller than Tb, in other words, Tb is 1.4x larger, right?
 
Last edited:
Physics news on Phys.org
  • #2
My approach would be to solve the formula for T:
T1 = 2π*sqrt(mR/F)
I wrote that T1 to indicate it is the original period.
When R is doubled, you get
T2 = 2π*sqrt(m2R/F) and I wish I could make that 2R a red 2 to make it easier to follow. That 2 needs to go out of the sqrt where it becomes a root 2 and move to the front so you can see
T2 = sqrt(2)*2π*sqrt(mR/F) = sqrt(2)*T1
It is an excellent technique; works every time!
 

1. What is uniform circular motion?

Uniform circular motion is the motion of an object traveling in a circular path at a constant speed, where the direction of motion is constantly changing.

2. What is the relation between the speed and radius in uniform circular motion?

In uniform circular motion, the speed of the object is directly proportional to the radius of the circular path. This means that as the radius increases, the speed of the object also increases, and vice versa.

3. How is acceleration related to uniform circular motion?

In uniform circular motion, the acceleration is directed towards the center of the circle and is called centripetal acceleration. It is proportional to the square of the speed and inversely proportional to the radius of the circular path.

4. What is the difference between angular velocity and linear velocity in uniform circular motion?

Angular velocity is the rate of change of the angle of rotation, while linear velocity is the rate of change of the distance along the circular path. In uniform circular motion, the two velocities are related by the formula v = ωr, where v is linear velocity, ω is angular velocity, and r is the radius of the circle.

5. How does the mass of an object affect its motion in uniform circular motion?

The mass of an object does not affect its motion in uniform circular motion. As long as the object is moving at a constant speed and following a circular path, its mass has no influence on its motion. This is because the centripetal force required to maintain the circular motion is provided by the object's velocity and the radius of the circular path, not its mass.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
633
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
602
  • Introductory Physics Homework Help
Replies
3
Views
890
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
8
Views
2K
Back
Top