Rotating object: Finding Tension and Vtheta

In summary, the problem involves a string with a 2kg mass on the end connected to a rotating bar at a constant rate. The string forms a constant angle of 60 degrees with the horizontal plane. The goal is to find the value of theta dot and the tension force in the string. Using the equations F(z) = 0 and F(n) = ma(n), the tension force was determined to be 22N. The value of 'v' was then found using the second equation and a p value of 1.57. Finally, theta dot can be determined using the value of 'v'.
  • #1
bjno8
2
0

Homework Statement


A string with 2kg mass m on the end is connected to a bar that rotates at a constant rate (theta dot). The string makes a constant angle beta, = 60 degrees relative to the horizontal plane. Find theta dot and the tension force in the string.


Homework Equations





The Attempt at a Solution



I realize this may be very difficult to understand without a picture, but the rotation is in the x y direction I suppose and gravity is acting downward in the Z direction. I'm not really sure how to go about this problem. There's a specific velocity that will give the angle relative to the x-axis the 60 degrees but I'm quite stuck, any help would be great.
 
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  • #2
Maybe this is right?

Ok so after fighting through it again, I realized what might work...

F(z) = 0; Tcos(30) - 2kg*9.81 = 0: T = 22 N

F(n) = ma(n); 22sin(30) = 2(v^2/1.57)

I realized I also forgot to mention the p value: 1.57
 
  • #3
bjno8 said:
Ok so after fighting through it again, I realized what might work...

F(z) = 0; Tcos(30) - 2kg*9.81 = 0: T = 22 N

F(n) = ma(n); 22sin(30) = 2(v^2/1.57)

I realized I also forgot to mention the p value: 1.57
Looks good so far. The solution of the 2nd equation will give you 'v'. After determining what 'v' represents, you must now determine theta dot.
 

1. What is tension in a rotating object?

Tension in a rotating object refers to the force that is exerted on the object in order to keep it in a circular motion. It is directed towards the center of the circular path and is responsible for the object's centripetal acceleration.

2. How is tension calculated in a rotating object?

Tension can be calculated using the equation T = mv^2/r, where T is the tension, m is the mass of the object, v is its linear velocity, and r is the radius of the circular path. This equation is derived from Newton's second law of motion, which states that the sum of all the forces acting on an object is equal to its mass times its acceleration.

3. What is Vtheta in a rotating object?

Vtheta, also known as angular velocity, is the rate at which an object rotates around a fixed axis. It is measured in radians per second and is related to the object's linear velocity by the equation v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity.

4. How do you find the tension and Vtheta in a rotating object experimentally?

To find the tension and Vtheta experimentally, you can use a device called a dynamometer, which measures the force exerted on a rotating object, and a tachometer, which measures the angular velocity of the object. By collecting data from these devices, you can use the equations mentioned in the previous questions to calculate the tension and Vtheta of the rotating object.

5. Why is tension important in a rotating object?

Tension is important in a rotating object because it is the force that keeps the object in circular motion. Without tension, the object would move in a straight line tangent to its circular path. Additionally, tension is directly related to the object's angular velocity, which is crucial in understanding the object's motion and dynamics.

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