A simple angular velocity with two spheres problem

In summary, two masses with the same mass m are tied together by a string and placed in a hollow cylinder. When the cylinder is rotated to an angular speed of ω, the tension in the string is T. If the string breaks, both masses will move away from the axis in the cylinder. The equation for tension is T=mrω^2, regardless of the number of masses attached.
  • #1
dennislam
5
1

Homework Statement


Two masses have same mass m, both of them are tied by a string and put in a hollow cylinder.
When the cylinder start to rotate until the angular speed is ω.
The tension in the string is T and the string breaks, both masses move away from the axis in the hollow cylinder.

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Homework Equations


T=mrω^2

The Attempt at a Solution


I have no idea about whether the tension T is equal to mrω^2 or 2mrω^2 (since there is two masses)
Please help!:cry:
sorry for my bad english
 
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  • #2
If you pull a spring with a force F, the spring pulls back with a force F. The tension in the spring is F, not 2F.
Same with a rope. In the situation described, but e.g. also if the rope hangs over a pulley and the two masses both pull down with ##mg##. Tension is ##mg##, not ##2mg##
 

FAQ: A simple angular velocity with two spheres problem

1. What is angular velocity?

Angular velocity is a measure of the rate of change of angular displacement over time. It is commonly represented by the symbol ω (omega) and is measured in radians per second.

2. How is angular velocity different from linear velocity?

Angular velocity is a measure of rotational motion, while linear velocity is a measure of straight-line motion. Angular velocity is also a vector quantity, meaning it has both magnitude and direction, while linear velocity only has magnitude.

3. What is the difference between angular velocity and angular speed?

Angular velocity and angular speed are often used interchangeably, but they are slightly different. Angular velocity is a vector quantity, while angular speed is a scalar quantity. Additionally, angular velocity takes into account the direction of rotation, while angular speed does not.

4. How can angular velocity be calculated?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. It can also be calculated by multiplying the angular speed by the radius of rotation.

5. How can the simple angular velocity with two spheres problem be solved?

The simple angular velocity with two spheres problem can be solved by using the law of conservation of angular momentum. This states that the total angular momentum of a system remains constant unless acted upon by an external torque. By setting the initial angular momentum of the system equal to the final angular momentum, the angular velocity of the spheres can be calculated.

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