Gear Ratio in Bicycles using Rotational Motion

[A.T.]

What does it have to do with physics?

Physics describes levers quite well.

 

[andyrk]

I don't understand how the fact that it becomes harder or easier to pedal, can be explained by physics.

 

[A.T.]

I don't understand how the fact that it becomes harder or easier to pedal, can be explained by physics.

Do you understand it for levers? Pushing down at different points of a playground seesaw?

 

[andyrk]

Do you understand it for levers? Pushing down at different points of a playground seesaw?

Yes I know it becomes tougher or easier. But how do you relate it to circular motion and what part of circular motion would it use? Torque? The relation between angular velocity and tangential velocity? What?

 

[A.T.]

But how do you relate it to circular motion and what part of circular motion would it use?

I would start with a static case, and try to understand the relation between applied forces (that's what you "feel").

 

[sophiecentaur]

Yes I know it becomes tougher or easier. But how do you relate it to circular motion and what part of circular motion would it use? Torque? The relation between angular velocity and tangential velocity? What?

Do you see a connection between gears and levers (and all other machines, in fact)? Have you actually read any basics of this or are you trying to get your education just by asking questions here on PF. That is a very inefficient method of learning.

 

[russ_watters]

Also, when we change gears, why does it become easier to pedal(less effort, pedals feel lighter) or difficult to pedal (more effort, pedals feel heavier), depending on the gear we shifted to? Does this have any physics related to it?

This:

It changes the ratios of angular velocities and torques, between back wheel and pedals.

Also: https://en.wikipedia.org/wiki/Mechanical_advantage
That discusses both levers and gears...and pulleys. Pick whichever one makes the most intuitive sense to you to start off with -- they all do the same thing from an "easier/difficult" perspective.

Or, another way: changing gears changes the length of the "lever arms" that transmit the torque.

 

[Chestermiller]

It boils down to two moment balances, one on the pedal axle (and attached front gear) and the other on the rear wheel axle (and attached rear gear). The chain attaches to both gears and transmits torque between them. It is able to do this because the tension in the upper part of the chain becomes higher than the tension in the bottom part of the chain. Does this contain enough physics in it for you?

Draw a free body diagram of the rear wheel with the chain split top and bottom at some location between the rear axle and the pedal axle. Then draw a free body diagram of the pedal axle with the chain split at the same location

Chet

 

[andyrk]

Why should two gears connected by the same chain rotate with the same torque?

 

[russ_watters]

Why should two gears connected by the same chain rotate with the same torque?

They don't. Again, read this:

It changes the ratios of angular velocities and torques, between back wheel and pedals.

 

[Chestermiller]

Why should two gears connected by the same chain rotate with the same torque?

As Russ said, the torques are not the same. You would already know this if had followed my suggestion in post #58 and drawn the free body diagrams that I indicated. This is a very straightforward system to analyze if you use the free body diagrams. Show us what you can do. On the other hand, if you feel that you have advanced beyond the point where you need to use free body diagrams, I think you will now agree that you haven't.

Chet

 

[andyrk]

As Russ said, the torques are not the same. You would already know this if had followed my suggestion in post #58 and drawn the free body diagrams that I indicated. This is a very straightforward system to analyze if you use the free body diagrams. Show us what you can do. On the other hand, if you feel that you have advanced beyond the point where you need to use free body diagrams, I think you will now agree that you haven't.

Chet

No I can understand it by drawing the FBD. But I am studying this just for fun and I am lazy, so I don't want to bother with FBD and instead understand it just by discussion. But if that won't make me understand this completely, then I would have no other option than to draw the FBD. But I am just waiting till then.

 

[Chestermiller]

No I can understand it by drawing the FBD. But I am studying this just for fun and I am lazy, so I don't want to bother with FBD and instead understand it just by discussion. But if that won't make me understand this completely, then I would have no other option than to draw the FBD. But I am just waiting till then.

You've already waited too long. Your admitted laziness has cost those of us who are trying to help you lots of our valuable time. Doesn't that matter to you?

Chet

 

[russ_watters]

Semi-rhetorical question: it matters to us.

We've been humoring you based on the possibility that you might be young or slow, but lazy is something we can't abide.

This thread has gone around in circles long enough and is therefore locked. Tomorrow, when you have another question on the subject, reread the thread; I suspect you will find that it has already been answered.