Center of Rotation w/ 4 Objects: Finding Tension

In summary, the conversation discusses finding the center of rotation and tension in a system of objects of equal weight and massless rods. The center of rotation is easily determined, but determining the tension requires using the net force and centripetal force equations. It is found that the tension on the middle object must be 2N, while the tension on the side objects is 4N and 5N. There is some confusion about whether the tensions should be the same for both sides, but it is ultimately determined that they can differ due to the net force being different for each side.
  • #1
SS2006
80
0
If w = 1.0 rad/s


0-----0-----0-----0

lenght 1 = 2 m
lenght 2 = 3 m
lenght 3 = 4 m

each circl is a object weighing 1 kg.

find center of rotation

and tension in the massless rods


getting center of rotation was easy
but tension..
well i know if there's 3 objects, to get tension, i used m*wsquare*r from each object to the center of rotation giving me 2 tensions, that worked, but with 4 objects, what do we do here. ( iknow we should get 3 tensions)
 
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  • #2
It's much easier than you might think. After solving for the outer tensions. Look at one of the "inside masses." The ouside tension is pulling outward, and the inside tension pulls inward. The net force here must be centripetal force. If you did things correctly, it doesn't matter which inner mass you choose, because the tension must be the same on each (tension pulls equqally at both ends).
 
Last edited:
  • #3
is this right then?

t1 = 4 N

t3 = 5N

t2 = 1 N (difference between 2 ends?)

letmeknow thanks
 
  • #4
YOu have 1 and 3 correct, but the middle tension is not.

call the four particles a, b, c, d.

You can see that the centripetal force on the c must be 1 N right? Well, in perfect uniform circular motion, the centripetal force must be the net force. Tension 3 is pulling on c to the right with 5N (since 5 N is pulling on d at the other end), but the net force on c must be 1 N. How much must tension 2 be to make it so? You find the same answer if you use the same longic on b.
 
  • #5
i get 4 N when using C
and 6N when using B
shudnt they be teh same


for C
-fnet + 5 =1
fnet = 4

for b

-4 + fnet = 2
fnet = 6
 
  • #6
SS2006 said:
i get 4 N when using C
and 6N when using B
shudnt they be teh same
for C
-fnet + 5 =1
fnet = 4
for b
-4 + fnet = 2
fnet = 6
For c:

Fnet = 1N
Fnet= T2 - 5N = 1N
(5N is T3 on d)

For b:

Fnet = 2N
Fnet = T2 - 4N = 2N
(4N is T1 on a)
 

1. What is the center of rotation in a system with four objects?

The center of rotation is the point around which all four objects rotate. It is the common point of rotation for all the objects in the system.

2. How is the center of rotation determined in a system with four objects?

The center of rotation can be determined by finding the point where the tension forces from all four objects intersect. This can be done by drawing a free body diagram and using trigonometry to find the angles and distances between the objects.

3. Why is it important to find the center of rotation in this system?

Finding the center of rotation is important because it allows us to calculate the tension forces acting on each object. It also helps us understand the overall rotational motion of the system.

4. How does the tension in the ropes change as the objects rotate around the center of rotation?

The tension in the ropes will change as the objects rotate around the center of rotation. As the objects move closer to the center, the tension will increase, and as they move away from the center, the tension will decrease.

5. Are there any assumptions made when finding the center of rotation in this system?

One common assumption is that the ropes are massless and do not stretch. This allows us to simplify the calculations and focus on the rotational motion of the objects.

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