Calculating Net Torque in a Rotating System

• checkmatescott
In summary, the conversation is about finding the total net torque and work done as a weight moves around a quarter circle. The individual is struggling to explain their idea and is unsure of the correct question to ask. They want to find the total/average torque and multiply it by the angle to get the total joules of work done. However, it is pointed out that finding the change in gravitational potential energy would be a more direct approach to calculating the work. The individual also mentions wanting to find the initial and final torque, but it is unclear why they need this information. The conversation ends with a question about whether to use radians or degrees in the calculations.
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

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• problem diagram.jpg
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checkmatescott said:

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.

checkmatescott said:
i think i have to take an integral
Integral with respect to what variable? Please post the complete problem statement.

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

checkmatescott said:
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?

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• torc.gif
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checkmatescott said:
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.

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

checkmatescott said:
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.

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

checkmatescott said:
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.

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

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• torque to displacement.jpg
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• torque to displacement.jpg
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and also do you divide the angle in rads or degrees thanks again for your time

checkmatescott said:
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?
checkmatescott said:
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?

both

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

checkmatescott said:
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?

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

checkmatescott said:
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?

by the way this wasn't homework

checkmatescott said:
by the way this wasn't homework
Are you still interested in the answer?

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

checkmatescott said:
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.

What is net torque in a rotating system?

Net torque is the measure of the rotational force acting on an object in a rotating system. It is the product of the applied force and the distance from the axis of rotation to the point where the force is applied.

How do you calculate net torque?

To calculate net torque, you need to determine the magnitude and direction of each individual torque acting on the object, and then sum them together. The formula for net torque is: τnet = Στ, where τ is the individual torque and Σ is the sum of all torques.

What are the units of net torque?

The units of net torque are newton-meters (N*m) in the SI system and foot-pounds (ft*lbs) in the imperial system.

What factors affect the net torque in a rotating system?

The net torque in a rotating system is affected by the magnitude and direction of the applied forces, as well as the distance between the axis of rotation and the point where the force is applied.

How is net torque related to rotational equilibrium?

In a rotating system, net torque is related to rotational equilibrium. If the net torque is zero, the object will remain in a state of rotational equilibrium and will not rotate. If the net torque is non-zero, the object will experience rotational acceleration and will rotate in the direction of the net torque.

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