Find Tension in a Cable with Rotational Mass

In summary, the conversation discusses finding the tension in a cable attached to a free falling cylinder with mass m and radius r. The formula for calculating angular acceleration is given as torque divided by inertial, and the tangential force is equal to the torque. The torque is also equal to inertial times r or m*r^3. The resulting equation for tension is mg-ma, where a is the angular acceleration. The conversation then moves on to setting up the equation and identifying the forces acting on the cylinder.
  • #1
rtran
3
0
I read the rule and ran a search with no luck.

How do i find the Tension in a cable?
I got a free falling cylinder with mass m and radius r

according to the formula a=torque/inertial and the tangential force is=to torque.
the torque =inertial*r

So i got angular acceleration = F*r/(m*r) and Tension=mg-ma
 
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  • #2
Please define the problem completely. Don't know what you mean by a "free falling cylinder".
 
  • #3
I read the rule and ran a search with no luck.

How do i find the Tension in a cable?
I got a free falling cylinder with mass m and radius r attach to a stationary string

according to the formula angular acceleration=torque/inertial and the tangential force is=to torque.

the torque =inertial*r or m*r^3

So i got angular acceleration = F*r/(m*r) and Tension=mg-ma

How exactly do i setup this equation to find the tension?
 
  • #4
sorry the rest must have timed out

A free falling cylinder is attached to a stationary string.

I got as far as torque =F*r=mgr which also equal to mr^2*angular acceleration.
The tangentail force =Tensioner which is ma , but I can't seem to put everything togather.
 
  • #5
I merged the two threads that you started... (I will move this to the Intro Phys section)

Start by identifying the forces acting on the cylinder. Compare translational acceleration and rotational acceleration, applying Newton's 2nd law to each.

rtran said:
I got as far as torque =F*r=mgr which also equal to mr^2*angular acceleration.
I don't understand what you did here. What's the torque about the center of mass? What's the rotational inertia of a cylinder?
 

1. How is tension in a cable with rotational mass calculated?

The tension in a cable with rotational mass is calculated using the formula T = mω²r, where T is the tension, m is the mass, ω is the angular velocity, and r is the radius of the circular motion.

2. What factors affect the tension in a cable with rotational mass?

The tension in a cable with rotational mass is affected by the mass of the object being rotated, the speed of rotation, and the distance from the axis of rotation to the point where the cable is attached.

3. Can the tension in a cable with rotational mass ever be zero?

No, the tension in a cable with rotational mass cannot be zero. Even if the object is not rotating, there will still be a minimum tension in the cable to support the weight of the object.

4. How is the tension in a cable with rotational mass different from a regular cable tension?

The tension in a cable with rotational mass is different because it takes into account the additional force needed to rotate the object, in addition to the weight of the object. This means that the tension in a cable with rotational mass will be greater than the tension in a regular cable supporting the same object.

5. What are some real-life applications of finding tension in a cable with rotational mass?

Knowing the tension in a cable with rotational mass is important in a variety of situations, such as determining the strength of cables used in amusement park rides, calculating the force needed to rotate a satellite in space, and designing cranes and other heavy machinery that use cables for lifting and rotation.

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