Circular Motion, Moments, Levers and Gears

The centripetal force always acts perpendicular (at $90^\circ$) to the direction of instantaneous motion, directed towards the centre of the circular path. Because the force acts at a right angle to the movement, it does no work in the direction of motion, meaning it only changes the direction of the velocity vector without altering the speed.

If the centripetal force is suddenly removed (for example, if a string snapping), the object will continue to move in a straight line at a tangent to the circle due to its inertia. The amount of centripetal force required to keep an object in circular motion increases if the mass or speed of the object increases, or if the radius of the circle decreases.

Moments: The Turning Effect of a Force

Have you ever noticed how much easier it is to open a heavy door if you push near the handle rather than near the hinges? This happens because you are creating a larger turning effect.

A moment is defined as the turning effect of a force about a fixed point, known as a pivot (or fulcrum). When calculating a moment, the distance used must always be the perpendicular distance from the pivot to the line of action of the force.

If an object is balanced and not turning, it is in rotational equilibrium. In this state, the total clockwise moment must perfectly equal the total anticlockwise moment about the same pivot.

The equation for calculating a moment is:

$$M = F \times d$$

Where:

• $M$ = Moment in Newton metres ($N\ m$)
• $F$ = Force in Newtons ($N$)
• $d$ = Perpendicular distance in metres ($m$)

A mechanic uses a spanner to loosen a tight nut. They apply a force of $45\ N$ at a perpendicular distance of $0.30\ m$ from the centre of the nut. Calculate the moment applied to the nut.

Step 1: Identify the values given in the question.

• $F = 45\ N$
• $d = 0.30\ m$

Step 2: Substitute these values into the moment equation.

• $M = 45 \times 0.30$

Step 3: Calculate the final answer and include the correct units.

• $M = 13.5\ N\ m$

Levers and Gears: Multiplying Forces

A simple metal bar can allow a single person to lift a boulder weighing hundreds of kilograms. Both levers and gears are simple machines designed to transmit rotational forces, making physical tasks easier to perform.

Levers and gears often act as a force multiplier, meaning they produce an output force that is greater than the input force. In a lever system, the input force is called the effort, and the output force applied to the object is the load.

Because a moment depends on both force and distance, applying a small effort at a large distance from the pivot creates a large turning effect. This can balance or lift a very large load located much closer to the pivot.

Gears achieve a similar effect using interlocked toothed wheels, which always rotate in opposite directions. When a smaller gear (the driver) turns a larger gear (the driven gear), it acts as a force multiplier. The larger gear produces a greater moment but rotates at a slower speed.

Conversely, if a large gear turns a smaller gear, it acts as a speed multiplier. The smaller gear will rotate much faster, but it will transmit a smaller turning effect (torque).

The gear ratio dictates exactly how the forces and speeds change. The ratio of the number of teeth on the gears is equal to the ratio of their radii. For example, if a driver gear has 15 teeth and the driven gear has 45 teeth, the driven gear has three times the turning effect but will rotate at one-third of the speed.

It is important to remember that these systems do not create free energy. Due to the conservation of energy, the total work done ($Force \times Distance$) remains constant. Using gears or levers to multiply force helps to easily overcome the inertia of a heavy object, but the effort must move through a proportionately larger distance to compensate.