Calculating Net Torque in a Rotating System

[checkmatescott]

Homework Statement

hi my question is that say if rod of length l is 3m and is 90 degrees from horizontal pointing upwards with 2 kg weight on the end then there will be no torque produced because the force of gravity is acting parallel to the lever arm if the angle theta is 80 degrees then the torque would be weight force x l sin theta giving the lever arm x and if the rod was horizontal then the torque would be the weight force x l because the weight force would be acting perpendicular to the lever arm ie its maximum length i think i have to take an integral but I am not sure how i know that the torque increases as x increases but i don't know how to do it I am really stuck i want to find the total net torque as the weight moves around the quarter circle can anybody help it would be much appreciated thanks in advance i can provide a diagram if that would help you to get what I am talking about

 

[berkeman]

Homework Statement

hi my question is that say if rod of length l is 3m and is 90 degrees from horizontal pointing upwards with 2 kg weight on the end then there will be no torque produced because the force of gravity is acting parallel to the lever arm if the angle theta is 80 degrees then the torque would be weight force x l sin theta giving the lever arm x and if the rod was horizontal then the torque would be the weight force x l because the weight force would be acting perpendicular to the lever arm ie its maximum length i think i have to take an integral but I am not sure how i know that the torque increases as x increases but i don't know how to do it I am really stuck i want to find the total net torque as the weight moves around the quarter circle can anybody help it would be much appreciated thanks in advance i can provide a diagram if that would help you to get what I am talking about

Do you have a diagram that you can post? Use the Upload button in the lower right of the Edit window to upload a JPEG or PDF copy of your diagram. Thanks.

 

[haruspex]

i think i have to take an integral

Integral with respect to what variable? Please post the complete problem statement.

 

[checkmatescott]

im trying to explain the best i can i have posted a picture as the length x changes with respect to the weight falling round the arc of the circle the torque will increase because the lever arm is getting longer the further from the top it gets to be honest i don't know the right question to ask i have an idea in my head but I am struggling to explain it

 

[berkeman]

i have posted a picture

If I read the diagram correctly, the mass is constrained to travel along the circle? But then why is your "line of action" vertical?

 

[checkmatescott]

 

[haruspex]

im trying to explain the best i can i have posted a picture as the length x changes with respect to the weight falling round the arc of the circle the torque will increase because the lever arm is getting longer the further from the top it gets to be honest i don't know the right question to ask i have an idea in my head but I am struggling to explain it

The trouble is that "total net torque" is undefined until you specify the variable with respect to which you are summing. Could be time, angle, x displacement, y position, ... and these will all yield different answers.
If you could explain why you want to find the total (or average) we might be able to advise on which variable.

 

[checkmatescott]

i want to find the total/average torque because i then want to multiply by the angle the weight has turned to get the total joules available to do work thanks for the speedy responses btw all i know is that when the effective lever arm x increases so does the torque hope this makes sense

 

[haruspex]

i want to find the total/average torque because i then want to multiply by the angle the weight has turned to get the total joules available to do work thanks for the speedy responses btw all i know is that when the effective lever arm x increases so does the torque hope this makes sense

Then you don't want the average torque after all - the calculation would involve finding the work done then dividing by the angle!
So let's just concentrate on what you really want, the work done. Consider the change in gravitational potential energy.

 

[checkmatescott]

ok thanks for that but shouldn't the gravitational potential energy be = to the average torque x the angle i want them to be the same answer ideally

 

[haruspex]

ok thanks for that but shouldn't the gravitational potential energy be = to the average torque x the angle i want them to be the same answer ideally

Yes, that is what I meant. You can use change in GPE to calculate the work then, if you wish, divide by the angle to find the average torque. But you posted that the work is what you wanted to find, so going on to find the average torque is somewhat redundant.

 

[checkmatescott]

ok got it how do you then find the initial torque and the final torque

 

[checkmatescott]

and also do you divide the angle in rads or degrees thanks again for your time

 

[haruspex]

ok got it how do you then find the initial torque and the final torque

Why do you want to find those? How do you plan to use that information?

do you divide the angle in rads or degrees thanks again for your time

This is confusing.
In post #8 you stated that you only wanted to find the average torque in order to find the work done. I have explained twice now that it is the other way around: if you wanted to know the average torque you would first have to find the work done, and since what you really want to find is the work done there is no point in finding the average torque at all. Yet here again you seem determined to find the average torque.
Please clarify: is it the work done you need to find, or the average torque, or both?

 

[checkmatescott]

both

 

[checkmatescott]

i think i need the equation dx/dy dx being the change in effective lever arm and dy being the change in torque its just a shot in the dark i really need help and advice

 

[haruspex]

both

Ok, but it is really helpful if you state up front everything you are to find. I see you posted a sketch of a graph of torque versus x (whatever x represents there) and ask about initial and final torque. Am I to infer that you are required to sketch such a graph?

Anyway, please put that aside for now and concentrate on finding the gravitational work done.
What are the initial and final angles of the movement?

 

[checkmatescott]

initial angle 0.75 rad from horizontal final angle 0 rad turning in the clockwise direction

 

[haruspex]

initial angle 0.75 rad from horizontal final angle 0 rad turning in the clockwise direction

So what is the loss in gravitational potential energy?

 

[checkmatescott]

by the way this wasn't homework

 

[haruspex]

by the way this wasn't homework

Are you still interested in the answer?

 

[checkmatescott]

yes if i remember right i wanted to know if you where on to of a pole say 5m would you be going faster a micro second before impact if you just dropped from the top of the pole or would you be going faster if you sat on the pole and waited for it to rotate 90 degrees to flat my thinking was that you would be going faster if you stayed sat on the polebecause you have to add in the centripetal accelleration

 

[haruspex]

yes if i remember right i wanted to know if you where on to of a pole say 5m would you be going faster a micro second before impact if you just dropped from the top of the pole or would you be going faster if you sat on the pole and waited for it to rotate 90 degrees to flat my thinking was that you would be going faster if you stayed sat on the polebecause you have to add in the centripetal accelleration

If the pole has no mass then by conservation of work your KE would be the same at the ground regardless of the route.
If the pole is anchored to a pivot at the base then your landing velocity will be vertical in both cases.