Tension in 3.14kg, 2m Radius Rope Spinning at 1 rad/sec

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In summary, a circle of rope with a mass of 3.14kg and a radius of 2 meters is rotating at 1 rad/sec with an axis through its center. The question is asking for the tension in the rope. To solve this, draw a diagram and consider a small element of the rope, which has tension on either side and experiences centripetal acceleration. By equating the sum of the two tensions to the centripetal force, you can solve for the tension in the rope. Be mindful of using the mass of the rope covering the small angle, not the entire rope.
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biketar827
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A circle of rope of total mass 3.14kg and a radius of 2 meters is spinning at an anglular velocity of 1 rad/sec about an axis through the center of the circle. What is the tension in the rope?

Thanks for the help, I'm having trouble getting this one. :eek:
 
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  • #2
biketar827 said:
A circle of rope of total mass 3.14kg and a radius of 2 meters is spinning at an anglular velocity of 1 rad/sec about an axis through the center of the circle. What is the tension in the rope?

Thanks for the help, I'm having trouble getting this one. :eek:

What have you done so far? Do you have any ideas?

EDIT: apologies. This is trickier than I first thought. I misunderstood the question.

HINT:
Draw a picture first.

Work on a small element of the rope. It covers a small angle [itex]d\theta[/itex]. It is undergoing centripetal acceleration. It has tension on either side of it. The two tensions add up to a centripetal force. Be careful with the vectors. Equating the sum of the two tensions, to the centripetal force you should be able to solve for T. Be careful to use the mass of the rope covering [itex]d\theta[/tex] Not the mass of the entire rope.

Hope this helps.
 
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The tension in the rope can be calculated using the formula T = mrω², where T is the tension, m is the mass, r is the radius, and ω is the angular velocity. In this case, we have m = 3.14kg, r = 2m, and ω = 1 rad/sec. Plugging these values into the formula, we get T = (3.14kg)(2m)(1 rad/sec)² = 6.28 N. Therefore, the tension in the rope is 6.28 N. I hope this helps! Let me know if you have any other questions.
 

1. What is tension in the rope spinning system?

The tension in the rope spinning system refers to the force applied by the rope on the object at its end. It is caused by the centrifugal force of the spinning motion and the weight of the object itself.

2. How is tension related to the mass and radius of the object?

The tension is directly proportional to the mass of the object and the square of the radius of the spinning motion. This means that as the mass or radius increases, the tension also increases.

3. How does the speed of rotation affect the tension in the rope?

The tension in the rope is directly proportional to the square of the rotational speed. This means that as the speed of rotation increases, the tension also increases.

4. What is the significance of 1 rad/sec in this system?

1 rad/sec (radian per second) is the unit of measurement for angular velocity, which is the rate of change of angular displacement. In this system, it represents the speed of rotation of the object at the end of the rope.

5. How can the tension in the rope be calculated?

The tension in the rope can be calculated using the formula T = m * r * ω^2, where T is the tension, m is the mass of the object, r is the radius of the spinning motion, and ω (omega) is the angular velocity.

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