-1

If I push an object in a linear way with constant force bigger than frictional force on ground, the object will accelerate more and more until air drag force matches it. Logically, If I add the same power to the object, its energy and of course its speed will increase continuously.

Why this doesn’t happen like this in rotational movements? If I rotate 1st gear(biggest) on bycle with the same power, wheels’ rpm is stuck after a short time and I have to shift to a smaller gear to get faster.

Actually, I’m adding the same power to the 1st gear continuously, but its angular speed doesn’t increase after a point. Why? I’m adding energy to system, where has it been gone?

If you push something on ground, it will accelerate continuously, but when it comes to rotation, they don’t accelerate after a specific angular speed even though you give the same energy you gave before.

Can you explain why?

Jawel7
  • 125
  • 5
  • Related – AJN Apr 10 '23 at 16:41
  • As I answered in the related question above, above a certain bicycle pedalling cadence (strokes per minute) your ability to add extra power will decrease. You can't keep up with the bike. You are not adding energy to the system anymore. You have passed the optimum speed for that gear. – Transistor Apr 10 '23 at 16:47
  • @Transistor I don’t understand. In formula P = Tw (TorqueAngular Speed), let’s say we indicated maximum angular speed and torque we applied on it at that RPM. Now, it means there is torque existing, but there is no acceleration! RPM is at the highest value, but there’s torque on system. Why rpm remains constant? – Jawel7 Apr 10 '23 at 17:47
  • "If I push an object in a linear way with constant force bigger than frictional force on ground, the object will accelerate more and more until air drag force matches it." No this is not true because you will never get there. You can't move your arms or legs fast enough for air drag to become the limiting factor unless it's something like a parachute. You are forgetting the speed of your legs or arm as you push. In the same way, a car whose wheels can produce all the torque in the world still will never go faster than the max RPM that the wheels can rotate at. – DKNguyen Apr 10 '23 at 18:59
  • "Now, it means there is torque existing, but there is no acceleration! RPM is at the highest value, but there’s torque on system. Why rpm remains constant?" Because the resistance to motion = Tw. – Transistor Apr 10 '23 at 22:02
  • @DKNguyen I see your point, but it doesn't explain difference between 1st and 2nd gear. Imagine that I have two objects with different mass(m1>m2). I started to push m1 with constant force and it accelerates up to my legs' maximum speed. I can't push more, because I can't touch the object if it accelerates more. That's fine. However, when I jumped a bit left and started to push m2 (lighter object), it will get faster than m1 and somehow, I can push m2 by exceeding my legs' maximum speed for m1. (When inertia decreases, angular velocity increases). How do you explain this? – Jawel7 Apr 11 '23 at 04:40
  • @Jawel7 Actuators such as muscles, engines, and motors all have a torque/force vs speed curve that they operate on. They can only produce a finite amount of power which means tradeoffs must be made between speed and force/torque. That means that for any given task, it is possible to have one thing in excess and not doing much good not having enough of the other, even though you theoretically can produce the power required. Each actuator has a point where the speed and torque/force correspond to maximum power, but to operate at this point the load must be matched to it. – DKNguyen Apr 11 '23 at 18:20
  • And that's why things like gearboxes such as the gears on your bike or the transmission in your car exists. – DKNguyen Apr 11 '23 at 18:21

2 Answers2

3

This gets back to the original answer by Tigerguy.
You have the maximum torque your legs can put out. You also have the maximum power your legs can put out (power = torque x rotational speed). But you ALSO have the maximum rotational speed that your legs are capable of. Typically 80-120 rpm for most people, though world class sprint racers can get up to twice that, for a short time.

When you are accelerating your bike, you reach one of those three limits, and then can't go any more. Either you've got to the maximum torque, or the maximum rotational speed, or you just maxed out on power.

Now, when you're in low gears, it's usually the maximum speed of your legs that you reach first. Now you can't go any faster, until you change up a gear. Or you train your legs to spin faster.

PatMc
  • 109
  • 3
2

This would work if input power could handle infinite speeds.

On a bicycle, your legs limit how fast you can pedal and the power you can input to the system. Motors have speed limits as well. The speed of a vehicle will increase until power equals resistance (wind plus road) or you hit a speed limiter. So first gear on a bicycle is no different from first gear in a car - you or the engine have maximum input speeds, so the vehicle has a maximum speed in first gear as well.

Internal combustion engines have increased friction as they speed up so they tend to have both natural maximum RPM, plus their design limits the desired maximum RPM. Electric motors will have similar limits. Simple DC motors have no-load speeds, and if the bearings won't handle this speed they need a limiter. AC induction motors are speed-limited by the electrical frequency and winding design. Your legs are limited by how the Creator or evolution made them.

Remember that power is speed times torque times a constant. What happens with your legs as that the amount of torque you can apply drops as your pedal cadence increases until both are at their maximum. Gears help balance your strength and speed to give max bike speed. Even a bike on a stand can only be pedaled so fast.

Tiger Guy
  • 7,376
  • 10
  • 22