Mechanical Reasoning Study Guide & Tips | Gears, Pulleys & Everything Between

When a belt or a chain connects to unmeshed cogwheels, both wheels will turn in the same direction. If the belt is crossed, they will turn in opposite directions.

In this case, the wheel’s velocity will be proportional to its radius rather than its number of teeth; aka its gear ratio:

• larger wheels will turn more slowly than smaller wheels. A larger wheel has a greater circumference and therefore covers a greater distance for every single turn, whereas a smaller wheel has to turn more than once in order to cover the same distance. The ratio of their diameters (or equivalently, the ratio of their radii) is directly proportional to the gear ratio and is inversely proportional to the ratio of wheel velocities.

When an internal cogwheel (light blue) and an external cogwheel (grey) are joined together, they will move in the same direction. However, the velocity-to-size ratio will remain as with internal cogwheels.

When a cogwheel connected to a toothed rack, the force is transferred from circular to linear. In this instance, the rack will move in the same direction as the wheel at the meshing point. The illustration above shows the cogwheel moving in a clockwise direction. At the meshing point, you can see that the wheel's direction is moving toward the left (red arrow). Because of the rack underneath will move to the left.

In general:

In a fixed pulley system, the load will move while the pulley does not. The pulley does not reduce the force needed to lift the load, it merely changes its direction.

In a moveable pulley system, the pulley will move along with the load. This, in turn, cuts the force of lifting the object and its weight in half.

As with gears, here there is also a trade-off. You will need half the force to lift the load, but double the amount of rope. E.g. to lift a load with a moveable pulley to a height of 1 meter, you will need 2 meters of rope. That rate increases as the number of pulleys increases.

These systems include more than one pulley and will either include both fixed and/ or moveable pulleys. In these systems, the force for lifting an object will be reduced but the distance for doing so will increase. The force required to lift the object is equal to the number of ropes supporting it.

A = lw

Area = πr2

R = Radius

Area = ½bh

B = Base

H = Height

Cuboid

V = b x h x w

Cylinder

V = πr2 x h

B = Base

H = Height

W = Width

R = Radius

Weight (W) x Distance (D1) = Force (F) x Distance (D2)

W = Weight

D1 = Distance from fulcrum to weight

F= Force required

D2= Distance from fulcrum to force point

N1/N2 = V2/V1

Or

N1 x V1 = N2 x V2

N1 = Number of teeth on wheel 1

N2 = Number of teeth on wheel 2

V1 = Velocity of wheel 1

V2 = Velocity of wheel 2

So if N1 = 8, N2 = 5. The gear ratio (1-2) will be = N1/N2 = V2/V1 = 8/5.

PV = nRT

P = Pressure

V = Volume

n = number of gas particles (amount of gas)

R = Gas constant (just a number)

T = Temperature

It should be noted that it is not as important to remember the formula exactly as it is important to know what it must hold. If a certain part of the equation changes, some other part must also change to maintain the equality (for instance, if the volume decreases, pressure must increase).

Ohm’s law states that the current passing through a conductor between two points is directly proportional to the potential difference across them.

I = V/R, or V = IR, or R = V/I

V = the potential difference measured across the conductor, in volts

R = the resistance of the conductor, in ohms

I = the current, in amperes

Another major part of a mechanical reasoning test will be questions concerning electrical concepts. These questions will come in the form of electrical circuit diagrams. Electrical circuits can be connected in two different ways: in series and in parallel. Examples of both types of circuits can be found below:

In Series

Components in series are connected along a single path so that the same current flows through all of them. In addition, the sum of the voltages each component develops is the total voltage produced in the system. Thus, it can be deduced according to Ohm's law that the total resistance of the system would be:

𝑅1 + 𝑅2 + ⋯ + 𝑅𝑛 = 𝑅τ

In a series circuit, a failure in any single component can potentially break the entire circuit as it breaks the flow of the electrical current.

In Parallel

Components in parallel are connected so that the same voltage is applied to each one. In a parallel circuit, the voltage across each of the components is identical, and the total current is the sum of the currents flowing through each of the components. Since the voltage of each component is identical but the currents add up, we again use Ohm’s law to deduce that the value of total resistance is:

1/𝑅1 + 1/𝑅2 + ⋯ + 1/𝑅𝑛 = 1/𝑅τ

In a parallel circuit it is possible for only one component to function when all others fail; thus the circuit will still function.

This is crucial! The guide included with our mechanical reasoning preparation materials deals exclusively with tests that assess your ability to understand and implement basic physical principles and concepts. Other mechanical tests, which require a higher academic level in physics, or specific vocational knowledge, require completely different studying methods.

Each test has its own priorities, obviously, but as a safe bet you could say that questions in a common mechanical test tend to be focused on the following subjects (ordered by prevalence from high to low):

• Force and moment
• Gears
• Wheels and pulleys
• Hydraulics
• Velocity and gravity
• Electrical circuits
• Thermodynamics
• Acoustics and optics

The bulk of the questions on mechanical tests are qualitative – meaning they are designed to assess your understanding of concepts, and not quantitative, which require calculations and accuracy.

It is extremely important to understand the underlying physical concepts that each question is based on. That way, you can "project" these concepts on new, never-seen-before situations.

Get ample practise. Our free online mechanical aptitude practice test only gives a glimpse of what our full PrepPack™ can give you. To ensure that you are able to pass your mechanical exam, we highly recommend using our full-length practice tests as they come with in-depth study guides and answer explanations aimed at improving your learning process. Practising with comprehensive materials will make all the difference.

Job level will determine test difficulty. Mechanical reasoning tests are used for many different jobs across several industries. These tests are often given for entry-level roles, but also for more experienced roles as well. Depending on the role you have applied for, the difficulty of your mechanical reason test is subject to increase. Our preparation materials can be used for a variety of job levels to ensure that you are getting the best practice possible.

Time management. Because mechanical aptitude tests are timed, it is best to answer each question in 30 seconds or less. Practising beforehand will help you to increase your speed and accuracy in answering the questions you will encounter.

Don’t stress. Giving yourself time to practice for your test beforehand will help you pass your test with confidence. There is no need to stress yourself out if you allow yourself to become familiar with the test structure, questions styles, and methods of answering.