I assume you know what Force is. Its unit is commonly Newton, or kg * meter / second^2. This comes from the famous formula F = m * A, where A = dV / dt.
If you have a rotating body and look at a point at a distance R (unit: meter) from the center, a force F applied to this point along the tangential direction of rotation causes a torque Q = F * R. Its unit is commonly in (Newton * meter). In the US, it's converted into (lb * ft), where lb is not a unit for mass, but a unit for force here.
The important thing to remember is that if two surfaces have a contact point and there is no slippage, then the forces on the two surfaces are equal at that point.
So, we have directly from the definition of torque:
(1) Torque_at_wheel = Force_at_wheel * Radius_of_wheel.
Now, consider two gears, A and B, joined at a point P. Suppose B's radius is K, and A's radius is 1. Since A makes K rotations for every rotation of B, K is the gear ratio. At the contact point P, since there is no slippage, the force on A must be equal to the force on B. Let F be this force. Then:
Torque_A = F * Radius_A = F * 1,
Torque_B = F * Radius_B = F * K.
Thus Torque_B = Torque_A * K, magnified by the gear ratio.
Next, consider two gears A and B joined at the center by a common shaft that forces them to rotate at the same speed. We have Torque_A = Torque_B, obviously.
There are obviously many gears and shafts that connect the engine's output disc (fly wheel) ultimately to the wheel, but if K is their combined gear ratio, then:
(2) Torque_at_wheel = K * Torque_at_engine.
It's simply that.
Energy conservation has nothing to do with this. Let's imagine we confine the car so that it cannot move, and put conveyor belts under the wheels, and apply a frictional force under the conveyor belts. If I twist the engine with my hands, the puny little torque I generate cannot overcome the friction force under the belts to cause the belt to move or the wheels to turn. Since there is no motion, I am obviously doing zero work and rpm remains constantly zero. But do you claim that I am not transfering any force to the wheels? You'll feel my force if you are asked to provide the frictional force under the belts with your hands.
If you have a rotating body and look at a point at a distance R (unit: meter) from the center, a force F applied to this point along the tangential direction of rotation causes a torque Q = F * R. Its unit is commonly in (Newton * meter). In the US, it's converted into (lb * ft), where lb is not a unit for mass, but a unit for force here.
The important thing to remember is that if two surfaces have a contact point and there is no slippage, then the forces on the two surfaces are equal at that point.
So, we have directly from the definition of torque:
(1) Torque_at_wheel = Force_at_wheel * Radius_of_wheel.
Now, consider two gears, A and B, joined at a point P. Suppose B's radius is K, and A's radius is 1. Since A makes K rotations for every rotation of B, K is the gear ratio. At the contact point P, since there is no slippage, the force on A must be equal to the force on B. Let F be this force. Then:
Torque_A = F * Radius_A = F * 1,
Torque_B = F * Radius_B = F * K.
Thus Torque_B = Torque_A * K, magnified by the gear ratio.
Next, consider two gears A and B joined at the center by a common shaft that forces them to rotate at the same speed. We have Torque_A = Torque_B, obviously.
There are obviously many gears and shafts that connect the engine's output disc (fly wheel) ultimately to the wheel, but if K is their combined gear ratio, then:
(2) Torque_at_wheel = K * Torque_at_engine.
It's simply that.
Energy conservation has nothing to do with this. Let's imagine we confine the car so that it cannot move, and put conveyor belts under the wheels, and apply a frictional force under the conveyor belts. If I twist the engine with my hands, the puny little torque I generate cannot overcome the friction force under the belts to cause the belt to move or the wheels to turn. Since there is no motion, I am obviously doing zero work and rpm remains constantly zero. But do you claim that I am not transfering any force to the wheels? You'll feel my force if you are asked to provide the frictional force under the belts with your hands.
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