Unit 1 - Engineering Principles

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• Further Education (Key Stage 5)

Unit 1 - Engineering Principles

Section A - Applied Mathematics

Section B - Mechanical Principles

Section C - Electrical & Electronics Principles

Circular measurement

a) Degree to Radian Conversion

Example

Questions

Extras

Radians to Degrees Conversion

Example

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Questions

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Extras

Length of Arc

ARC LENGTH

The arc length of a circle is calculated by multiplying the circumference of the circle by the fraction of the full circle that the arc represents. The formula for arc length is s = (θ/360) * 2πr if the central angle (θ) is in degrees, or s = rθ if the angle is in radians.

Example to find Arc Length when Angle is DEGREES

62.8 Degrees

Example to find Arc Length When Angle is given in RADIANS

Questions

Question 1: Calculating the length of a curved section

A decorative steel arch for a building entrance is a segment of a circle. The radius of the circle is 12 metres, and the central angle of the arch is 115°.

a) Calculate the length of the steel arch, in metres, to two decimal places.

Question 2: Finding the angle for a robotic arm

A robotic arm is designed to move along a circular path. The arm has a length of 75 cm from the pivot point (the centre of the circle). The arm needs to travel an arc length of 40 cm.

a) Calculate the central angle, in degrees, through which the arm must rotate to achieve this movement. Give your answer to one decimal place.

Question 3: Calculating belt length for a pulley system

A pulley system consists of two pulleys connected by a belt. The larger pulley has a radius of 20 cm, and the smaller pulley has a radius of 8 cm. The central angle of contact between the belt and the smaller pulley is 150°.

a) Calculate the length of the arc of contact on the smaller pulley.

Volume of Cylinder

The volume of a cylinder is found using the formula V = πr²h, where 'V' is the volume, 'π' (pi) is a mathematical constant (approximately 3.14159), 'r' is the radius of the circular base, and 'h' is the height of the cylinder.

A hollow cylindrical pipe has an external diameter of 15 cm, a wall thickness of 1 cm, and a length of 2 m. 

• a) Calculate the internal radius of the pipe in cm.

b) Calculate the volume of material used to make the pipe in cubic metres to two decimal places.

Volume of Cone

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Section B

Mechanical Principles

Direct Stress

Direct stress is the force per unit area on a material when the force is applied perpendicular (normal) to the cross-section.

FORMULA FOR STRESS

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