Torque and Gear Ratios Explained: How Lever Length and Gears Affect Rotation

Torque and Lever Arm Basics

Torque is the product of a force and its distance from the pivot. The video demonstrates this with a seized nut and two wrenches: a 30 centimeter wrench with 90 Newtons of force gives 27 Newton-meters of torque, while a 60 centimeter wrench with the same force yields 54 Newton-meters. This shows that a longer lever increases the rotational effect for the same push, effectively using a larger circle to turn a smaller one.

Circle Geometry and Speed

By changing the size of the circle on which we apply force, we change both torque and rotational speed. A longer lever increases torque but can reduce angular speed, illustrating the trade-off between force and motion in rotational systems.

Introduction to Torque and Lever Arms

The video begins by defining torque as a measure of the rotational effect produced when a force is applied at a distance from a pivot. It uses a wrench and a nut as a tangible example: a shorter, harder-to-turn lever requires more effort to free a seized nut, while a longer lever makes the same force more effective. The presenter calculates the torque for two scenarios to illustrate the relationship between lever length and rotational force: a 30 centimeter (0.3 m) wrench with 90 Newtons of force yields 27 Newton-meters of torque, and a 60 centimeter (0.6 m) wrench with the same 90 Newtons yields 54 Newton-meters. This simple arithmetic demonstrates how increasing the lever arm increases torque, effectively creating a larger circle to turn the same circular object.

The Lever Arm and Speed: Circle Geometry

The explanation emphasizes that changing the lever arm changes both torque and the speed of rotation. By describing the lever arm as a radius, the video shows how increasing the radius while applying the same force multiplies the torque. This is connected to the concept of turning a larger circle to rotate a smaller circle, which enhances the rotational torque but may influence angular velocity. The core takeaway is that the interaction between radius and force determines the mechanical advantage of a lever system.

Low Gear vs High Gear: Torque and Speed Trade-offs

Next, the video introduces gears as a means to translate torque and speed. A low gear provides high torque and low speed, while a high gear produces high speed and low torque. Using the bicycle analogy, the presenter explains why starting in a low gear helps overcome the initial resistance to motion and get the bicycle moving. As speed increases, you shift to higher gears to achieve greater rotational speed at the same pedaling effort. When climbing a steep hill, you shift down to a lower gear to maintain the needed torque for propulsion. The same principle applies to cars, where gear changes are used to balance acceleration and fuel efficiency as vehicle speed and terrain change.

Practical Applications: Bicycles and Cars

The video ties the physics to real-world driving and cycling. On a bike, starting in a low gear makes it easier to overcome static friction and begin movement; once the rider gains momentum, shifting to higher gears increases speed. On a car, the driver starts in the lowest gear and upshifts as the car accelerates, but shifts down when the terrain becomes steeper to maintain the necessary torque for climbing. These examples illustrate how engineers design transmission systems to keep an engine within its efficient operating range while delivering sufficient torque when needed, such as on hills or during acceleration.

Conclusion and Further Learning

The video ends by inviting viewers to continue exploring engineering concepts through more content from the Engineering Mindset channel, including social media channels and the Engineering Mindset website for additional lessons.