How to Calculate the Torque Needed to Stop a Gear System in 2 Seconds?

In summary, the equation you need to remember is ## \displaystyle \tau = \frac {d L } {d t} ##, where ## L ## is the angular momentum. The torque you need to apply to bring the system down to zero in 2 seconds is given by ## \displaystyle \tau = \frac {\Delta L} {\Delta T} ##.
  • #1
TheAustrian
165
7
Hi all... I'm new here...

Homework Statement


this is not a homework question, I'm just solving practice questions for exam preparation
Two wheels with masses M1 = 2 kg and M2 = 4 kg are connected.
The ratio is R1 = 5 cm and R2 = 10 cm
Considering an angular velocity of ωo = 10rads-1
for the small wheel and a constant angular acceleration of α = 1
rads-2

What will be the torque τ required to stop the system after 20 s within a
period of 2 s?

Homework Equations


T1ω2=T2ω1

and

P = E/t

The Attempt at a Solution



I already found the energies of the Gears,
E1= 1.125J and E2=2.25J
but I have no idea how to find the torque needed to stop them in 2 seconds. I'm not even sure if I'm on the right track. I have like 3-4 A4 sheets worth of work all scribbled on/crossed out...

actually my problem is that if I work out the Torques, their ratio comes out at 0.25 rather than 0.5, so I'm not sure what to do.
 
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  • #2
I think you could use the simple relationship between torque and angular momentum. Energy makes this more complicated than it needs to be.
 
  • #3
voko said:
I think you could use the simple relationship between torque and angular momentum. Energy makes this more complicated than it needs to be.

But how will that allow me to calculate the question?
 
  • #4
In 20 seconds the system will have a certain amount of angular momentum. You need to apply some constant torque to bring it down to zero in 2 seconds.
 
  • #5
voko said:
In 20 seconds the system will have a certain amount of angular momentum. You need to apply some constant torque to bring it down to zero in 2 seconds.


So I should work out time taken to get angular momentum to zero and work on from there?
 
  • #6
You are GIVEN this time: 2 seconds.
 
  • #7
voko said:
You are GIVEN this time: 2 seconds.


Sorry, I phrased myself wrongly here
I meant I should work out the Angular momentum to get to zero in the time-span of two seconds, and then I need to work from there? Is there a relationship that connects torque and angular momentum?
 
  • #8
Torque is the rate of change of angular momentum.
 
  • #9
voko said:
Torque is the rate of change of angular momentum.

With respect to time?
 
  • #10
Yes, with respect to time. Since you are preparing for an exam, I suggest that you review the fundamentals of rotary motion. The relationship between angular momentum and torque is the equivalent of Newton's law, and you must know it even if awaken in the middle of the night!
 
  • #11
I think I will just surrender, I do not see how Angular Momentum should come into the question, if it's Torque I must know...

Thanks for trying to help though.
 
  • #12
This is a pity.

The equation you should remember is ## \displaystyle \tau = \frac {d L } {d t } ##, where ## \tau ## is torque, and ## L ## is angular momentum. This is analogous to Newton's second law: ## \displaystyle F = \frac {d p} {d t} ##. Assuming the torque is constant, as the problem requires, this simplifies to ## \displaystyle \tau = \frac {\Delta L} {\Delta T} ##, where ## \Delta L ## is the change of angular momentum and ## \Delta T## is the period of time during which the change occurs.

## L = I \omega ##, where ## I ## is the moment of inertia and ## \omega ## is angular velocity. Knowing the moments of inertia of the two wheels and their angular velocity, you know the net angular momentum, and the rest is simple.
 

Related to How to Calculate the Torque Needed to Stop a Gear System in 2 Seconds?

What is a gear ratio torque problem?

A gear ratio torque problem refers to a situation where the torque, or rotational force, applied to a gear system is not ideal or desired. This can occur when the gear ratio, or the ratio of the number of teeth on the input gear to the number of teeth on the output gear, is not optimized for the desired output torque.

Why is gear ratio torque important?

Gear ratio torque is important because it determines the amount of force that can be transmitted through a gear system. A higher gear ratio torque means that more force can be applied to the output gear, while a lower gear ratio torque means that less force can be applied. This can have significant implications in the performance and efficiency of machines and devices that use gear systems.

How is gear ratio torque calculated?

To calculate gear ratio torque, you need to know the gear ratio and the input torque. The gear ratio is calculated by dividing the number of teeth on the output gear by the number of teeth on the input gear. The gear ratio torque is then calculated by multiplying the gear ratio by the input torque. For example, if the gear ratio is 2:1 and the input torque is 10 Nm, the gear ratio torque would be 20 Nm.

What are some factors that can affect gear ratio torque?

There are several factors that can affect gear ratio torque, including the gear ratio, the number of teeth on the gears, the material and design of the gears, and the lubrication of the gears. Additionally, external factors such as temperature and wear and tear can also impact gear ratio torque.

How can gear ratio torque problems be solved?

There are several ways to solve gear ratio torque problems, depending on the specific situation. One approach is to adjust the gear ratio by changing the number of teeth on the gears or using different size gears. Another solution may involve using stronger or more efficient gear materials. Proper lubrication and maintenance can also help to improve gear ratio torque. In some cases, it may be necessary to redesign the gear system to optimize the gear ratio for the desired torque output.

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