Torque, Lever Arms and Gear Ratios: How Torque Works in Wrenches, Bikes, and Cars

Torque is the turning force that makes things rotate. In this video, a wrench and a seized nut illustrate how lever length changes the torque produced for the same pushing force. A 0.3 m wrench with 90 N yields 27 newton-meters, while a 0.6 m wrench yields 54 newton-meters, demonstrating how a longer lever increases turning effort. The lesson then links torque to gear ratios, showing that low gears provide high torque and low speed, while high gears offer higher speed and less torque. Bicycle and car examples connect the math to everyday motion, explaining why starting in a lower gear helps get moving and why shifting up and then down a hill matters. The video invites you to explore more mechanical and automotive engineering content on Engineering Mindset.

Introduction to Torque and Lever Arms

Torque is the turning force that causes rotation. It is defined as the product of the applied force and the lever arm distance to the pivot. The video uses a seized nut and a wrench to show the effect of lever length on torque. This simple demonstration helps viewers understand why longer handles produce greater turning forces for the same push.

The Numbers Behind the Idea

In the example, applying 90 newtons of force at 0.3 meters from the pivot yields 27 newton-meters of torque. If the same 90 newtons are applied at 0.6 meters, the torque doubles to 54 newton-meters. This concrete calculation makes the concept tangible and shows how lever length directly affects the torque that can be delivered to rotate a stuck nut.

From Arm Length to Torque: The Circle Picture

The video frames the situation in terms of circles. Using a longer wrench enlarges the circle over which the force acts. A larger circle can apply more turning effect to the same object. The core idea is that torque depends on both the force and the radius, so increasing one while holding the other constant increases the rotational effect. The geometry also changes the rotation speed; a larger radius can slow down the angular speed of the driven component, depending on the mechanism's constraints.

Gears, Torque and Speed: The Trade-Off

The presenter introduces gears as a way to manage torque and speed. A low gear reduces speed but increases torque, making it easier to start moving or climb. A high gear increases speed but reduces torque, enabling higher speeds once motion starts. These trade-offs are central to many machines and are essential for understanding both bicycles and automobiles. The video uses bike pedaling as a familiar example, noting that starting in a high gear can be very difficult because the legs must spin quickly while the wheel lags behind. As you reach higher speeds, you may shift to higher gears to maintain performance, and when you encounter gradients you may switch back to lower gears to keep the vehicle moving forcefully.

Bicycles and Cars: The Real World Connection

The bicycle scenario is described as starting movement in a low gear and then shifting up as the rider gains speed. When facing a steep hill, the rider moves to a lower gear to maintain torque and control over acceleration. The same principle applies to cars, where drivers begin in a low gear and change up as the vehicle accelerates, then shift down when climbing hills. The video ties these everyday actions to the underlying physics of torque and gearing, illustrating how engineers design transmission systems to balance torque and speed across different driving conditions.

Conclusion and Call to Action

The video concludes with an invitation to explore more on the Engineering Mindset channel. Readers are encouraged to apply the same thinking to other mechanical systems and to seek additional videos that expand on the physics of motion, gears, and power transmission across engineering domains.

Key Takeaways

Torque depends on force and lever radius; Extending the lever increases torque for a given force; Gears provide a torque speed trade-off; Low gears favor torque and starting ability, high gears favor speed once moving; Real world examples with bikes and cars help build intuition about mechanical design and power transmission.