Cards | 10 |

Topics | Force Lines of Action, Gear Ratio, Gear Trains, Kinetic Energy, Power, Principle of Moments, Wedge, Wheel and Axle |

**Collinear** forces act along the same line of action, **concurrent** forces pass through a common point and **coplanar** forces act in a common plane.

The mechanical advantage (amount of change in speed or torque) of connected gears is proportional to the **number of teeth** each gear has. Called gear ratio, it's the ratio of the number of teeth on the larger gear to the number of teeth on the smaller gear. For example, a gear with 12 teeth connected to a gear with 9 teeth would have a gear ratio of 4:3.

Connected gears of different numbers of teeth are used together to change the **rotational speed** and **torque** of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE **linearly** while an increase in speed increases KE **exponentially**.

Power is the rate at which work is done, **P = w/t**, or work per unit time. The **watt (W)** is the unit for power and is equal to 1 joule (or newton-meter) per second. **Horsepower (hp)** is another familiar unit of power used primarily for rating internal combustion engines. A 1 hp machine does 550 ft⋅lb of work in 1 second and 1 hp equals 746 watts.

When a system is stable or balanced (**equilibrium**) all forces acting on the system cancel each other out. In the case of torque, equilibrium means that the sum of the anticlockwise moments about a center of rotation equal the sum of the clockwise moments.

The wedge is a moving inclined plane that is used to lift, hold, or break apart an object. A wedge converts force applied to its blunt end into force **perpendicular** to its inclined surface. In contrast to a stationary plane where force is applied to the object being moved, with a wedge the object is stationary and the force is being applied to the plane. Examples of a wedge include knives and chisels.

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the **ratio of the diameters of the wheels**. An example of a wheel and axle is the steering wheel of a car.