# Finding angular velocity for a rope to be cut

• Like Tony Stark
So, I would say that the second rope will actually be cut with less angular velocity.In summary, the equations show that the first rope will have a greater tension than the second rope until one of the ropes breaks. The value of ω for the first rope is 16.37 rad/s while the value for the second rope is 20.56 rad/s. Therefore, the second rope will be cut with less angular velocity.
Like Tony Stark
Homework Statement
The bodies shown in the picture spin on a horizontal plane, describing a circular path with constant acceleration. They're connected by ropes that resist ##1100 N## (each rope). Find the angular velocity when one of the ropes is cut.
Relevant Equations
Newton's equation
I wrote Newton's equations for each body (I took ##x## as the axis aligned with the tension)

##m_1##:
##x)f*_1 -T_1+T_2=0##
Where ##f*_1=\omega ^2 r_1##

##m_2##
##x)f*_2 -T_2=0##
##x)f*_2=T_2##
Where ##f*_2=\omega ^2 r_2##

I wrote that ##T_2=1100 N## and solved for ##\omega##, and I got ##\omega =20.56 \frac{rad}{s}##.

Then, I wrote ##T_2=f*_2## in the equation for ##m_1##, replace ##T_1=1100## and solved for ##\omega##. Doing so I found that ##\omega = 16.37 \frac{rad}{s}##.

So, the first rope will be cut with less angular velocity.

Is this right?

#### Attachments

• 20191004_234215.jpg
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This looks good to me. But note that your first equation (for ##m_1##) shows that ##T_1## is going to be greater than ##T_2## for any value of ##\omega## up until one of the ropes breaks.

## 1. What is angular velocity and why is it important in finding the correct rope length to cut?

Angular velocity is a measure of how fast an object is rotating around a fixed point. In the context of finding the correct rope length to cut, it is important because it determines the distance the rope will travel in a given amount of time.

## 2. How is angular velocity calculated for a rope?

Angular velocity for a rope can be calculated by dividing the angular displacement (change in angle) by the time it takes for the rope to rotate that amount.

## 3. What are the units for angular velocity?

The units for angular velocity are radians per second (rad/s) or degrees per second (deg/s).

## 4. How does the thickness and weight of the rope affect its angular velocity?

The thickness and weight of the rope can affect its angular velocity by adding additional resistance and changing the distribution of mass along the rope. This can impact the rope's ability to rotate at a certain speed or angle.

## 5. Is there a specific formula for finding the angular velocity for a rope to be cut?

Yes, the formula for finding the angular velocity of a rope to be cut is ω = Δθ/Δt, where ω is angular velocity, Δθ is the change in angle, and Δt is the time it takes for the rope to rotate that amount.

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