Why Doesn't the Line Extend to the Zero Point on the Angular Acceleration Graph?

[Kristjan Tervonen]

Homework Statement

I have an angular acceleration and torque graph.

I know it should be a straight line between the points, but my question is, if you extend the line toward the angular acceleration, why it doesn't go to the zero point? It is about 0,6.

Homework Equations

The Attempt at a Solution

I have thought that there is some other forces that doesn't let the acceleration to be so low. If there is no acceleration, then how there can be any torque? The torque is what's making the accelration as I have learned.

 

[David Lewis]

ε is angular acceleration?
M is torque?
f is speed?

 

[Kristjan Tervonen]

ε is angular acceleration
M is torque

f means like function, not speed.

 

[David Lewis]

So f is the moment of inertia?

Re-number the horizontal (torque) axis so the tick marks are evenly spaced.
Then make sure the locations of your data points are drawn to scale,
and the vertical axis passes through the origin (M=0).

Is the spool upon which the cord is wrapped freewheeling or powered?

 

[gneill]

Is this data gathered in lab? If so, can you descr

So f is the moment of inertia?

No. It just means that angular acceleration is a function of the torque. f is an unspecified general function in this instance.

Kristjan, was this graph made from data collected in an experiment? If so, can you describe the setup?

 

[Kristjan Tervonen]

Yes, it is data from an experiment.
I had to check the constitution of the rotational dynamics. I put on weights and then the machine showed me the time. After that I had to look how far up weights went. Just like in that picture. After that, using the formulas, I calculated torque, acceleration and also moment of inertia.

 

[gneill]

Yes, it is data from an experiment.
I had to check the constitution of the rotational dynamics. I put on weights and then the machine showed me the time. After that I had to look how far up weights went. Just like in that picture. After that, using the formulas, I calculated torque, acceleration and also moment of inertia.

The weights were going up, not down?

 

[Kristjan Tervonen]

Yes, they went up.

 

[haruspex]

Yes, they went up.

Then you need to explain more about the set-up. What is driving the weights up? Please explain everything in the diagram.

 

[kuruman]

The plot by @Kristjan Tervonen bothers me. The values on the horizontal (M) axis are not spaced equally apart. Unless the abscissa is linear, it is not obvious whether there is a linear dependence in the plotted data. Assuming that the numbers on the abscissa are the actual values of M, not tickmark labels, and that the labels next to the data points are the corresponding values of ε, I replotted the data (see below). Depending on the error bars of the experiment, the result could be construed as a straight line.

 

[Kristjan Tervonen]

I think I know the answer now. Torque's values are less lower. So in the reality the graph is very narrow and should then go to the zero point.

 

[gneill]

I think I know the answer now. Torque's values are less lower. So in the reality the graph is very narrow and should then go to the zero point.

I don't think that playing with the graph proportions is a valid way to make the issue go away. The differences in measured values for angular acceleration is smaller than the zero offset value, so it shouldn't be a precision issue. Here's a best-fit line drawn through the given data:

The offset might be attributable to a calibration issue (a systematic error) if the device or method for measuring the angular acceleration has an uncorrected bias.

 

[haruspex]

I don't think that playing with the graph proportions is a valid way to make the issue go away. The differences in measured values for angular acceleration is smaller than the zero offset value, so it shouldn't be a precision issue. Here's a best-fit line drawn through the given data:

View attachment 108949

The offset might be attributable to a calibration issue (a systematic error) if the device or method for measuring the angular acceleration has an uncorrected bias.

Or, considering that the first few points do project a reasonably straight line through the origin, some effect is inhibiting or underestimating the acceleration at the higher torques.

 

[Ivanov]

Yes, torque is responsible for acceleration, but you can have an object spining at a constant speed and torque would exist. It is the twist force.

 

[haruspex]

Yes, torque is responsible for acceleration, but you can have an object spining at a constant speed and torque would exist. It is the twist force.

Please explain more. How would an unbalanced torque not lead to an angular acceleration?

 

[Ivanov]

Please explain more. How would an unbalanced torque not lead to an angular acceleration?

a change in torque will lead to a change in ang. acceleration, yes. What I got from the initial question is how can there still be torque if there is no acceleration. Did I understand wrong?

 

[haruspex]

a change in torque will lead to a change in ang. acceleration, yes. What I got from the initial question is how can there still be torque if there is no acceleration. Did I understand wrong?

Yes, a change in torque will lead to a change in angular acceleration, and a nonzero net torque will lead to a nonzero angular acceleration. If there is no angular acceleration then there must be no net torque.

 

[Ivanov]

and a nonzero net torque will lead to a nonzero angular acceleration

Acceleration means there is a change in speed. Something can spin and have torque without changing its speed. Constant speed means positive torque and 0 acceleration

 

[haruspex]

Constant speed means positive torque and 0 acceleration

That's a pre-Newtonian view.
In linear motion, ΣF=ma. |ΣF|>0 implies |a|>0. Net force leads to acceleration. Constant speed means no net force.
Exactly the same in rotational motion. Στ=Iα. |Στ|>0 implies |α|>0. Net torque leads to angular acceleration. Constant angular speed means no net torque.