Mechanical Reasoning Study Guide | Gears & Pulleys and More

## How to Prepare for the Mechanical Aptitude Test

The most tried and true method for preparing for this and any other test will be to practise beforehand. Knowing what to expect and how to answer the questions you will encounter will give you a major advantage over other candidates.

Our free mechanical aptitude sample test can give you a baseline for the concepts and skill level required to pass your mechanical reasoning test. Want more in-depth mechanical aptitude test practice? Our full mechanical reasoning PrepPacks™ include dozens of practice questions, complete study guides, answer explanations and more to ensure that you are fully prepared come test day.

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## Mechanical Reasoning Test Questions and Answers

The purpose of a mechanical reasoning test is to evaluate your understanding and application of mechanical concepts to find solutions to a variety of mechanical scenarios. Questions that you will often encounter on a mechanical aptitude test include:

 Acceleration Applied maths Balancing scales Ballistics Circular motion Clamps Cogs Friction Gears Gravity Kinetic and potential energy Levers Magnetism Mechanical terminology Mirrors and reflection Pressure and weights Pulleys Screws Shafts Simple electrical circuits Spatial or visual relations Springs Tools of the trade Volumes Wheels and belts - -

Due to the wide range of topics covered by mechanical reasoning tests, it is no wonder that practising beforehand is crucial to a successful result. Through in-depth practice tests and study guides, our mechanical aptitude PrepPacks™ are designed to help you improve your knowledge and application of mechanical and electrical concepts, thus giving you the ability to pass your pre-employment exams with ease.

## Gears & Pulleys

A gear can be represented as either a wheel or cylinder. A major characteristic of these wheels/ cylinders are the cogs/ teeth running along their outside edges. The three main purposes of gears are to change the direction of motion, increase or reduce speed and force, or to transmit force.

Questions regarding gears will typically use the rules below to solve. The fundamental rules of thumb for solving mechanical reasoning questions concerning gears/ cogwheels are:

• If gears are connected (meshed), adjacent gears will move in the opposite direction. If there are an odd number of cogwheels, the last wheel will turn in the same direction as the first wheel. In a system with an even number of cogwheels, the last cogwheel will turn in the opposite direction of the first.

Consider the following example:

• Unmeshed (not physically touching) gears that are connected by a chain or belt will move in the same direction. If the chain is crossed,they will move in opposite directions:
• There is a trade-off between force and speed: more teeth – lower speed, more force.
• Less teeth – higher speed, less force.
• Gear ratio: N1/N2 = V2/V1 (N is the number of teeth on gear 1/2, V is the rotation velocity).

For more information regarding the types of questions on gears that you may encounter on your assessment, please see below:

#### Gears & Belts

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.

#### External Cogwheels

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.

#### Rack & Pinion

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:

### Pulleys

Pulley systems typically involve one or more wheels controlled by a cord/ rope/ belt. By changing the direction of force applied to the rope, pulleys can be used to lift heavy objects/ weights. There are a variety of different pulley systems that you will encounter during a mechanical aptitude assessment. These include:

#### Fixed Pulley

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.

#### Moveable Pulley

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.

#### Combined Pulley

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.

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## Important Formulas

It is wise to brush up on certain mechanical formulas when preparing for a mechanical aptitude test. Below are some examples of formulas that you should know prior to sitting a mechanical reasoning test:

Rectangle

A = lw

L = Length
W = Width
Circle

Area = πr2

Triangle

Area = ½bh

B = Base

H = Height

Cuboid

V = b x h x w

Cylinder

V = πr2 x h

B = Base

H = Height

W = Width

#### Leverage

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

#### Gear Ratio

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.

#### Ideal Gas Law

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).

#### Electricity

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

#### Series & Parallel Circuits

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.

See below an excerpt of the full mechanical reasoning study guide that holds invaluable tips and formulas to maximize your performance.

#### Mechanical Study Guide Excerpt From the PrepPack™

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## Tips and Shortcuts

Below you will find tips and examples of shortcuts that you may find useful to passing your mechanical exam.

#### Know Which Test You Will Be Taking

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.

#### Know Which Subjects Matter

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

#### Focus on Qualitative Rather Than Quantitative Questions

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.

#### Try to Understand Principles and Concepts, Not Instances

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.

#### Other Useful Tips for Passing Your Mechanical Test

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.