AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Students should be familiar with the rad as the unit of angle.
Full specification wording
Advantages of large diameter telescopes (A-level only): Students should be familiar with the rad as the unit of angle.
The radian is the SI unit of angle and is essential in astronomy because it links an angle to the arc it subtends.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The radian is the SI unit of angle and is essential in astronomy because it links an angle to the arc it subtends. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius, so θ = s ÷ r. A full circle is 2π rad, a straight line is π rad and a right angle is π ÷ 2 rad. Convert degrees to radians by multiplying by π ÷ 180, and radians to degrees by multiplying by 180 ÷ π. For example, 30° = 30 × π ÷ 180 = π ÷ 6 rad ≈ 0.524 rad. Radians are needed for the small-angle approximation θ ≈ λ ÷ D and for angular resolution, where θ must be in radians for the formula to work.
What earns the marks
- States that one radian is the angle subtended at the centre of a circle by an arc equal in length to the radius.
- Uses θ = s ÷ r to relate arc length, radius and angle in radians.
- Converts between degrees and radians using π rad = 180°, multiplying by π ÷ 180 or 180 ÷ π as appropriate.
- Recognises that a full circle is 2π rad and that a right angle is π ÷ 2 rad.
- Applies radian measure in astronomical calculations such as angular resolution or the small-angle approximation.
Common mistakes and how to put them right
Treating a radian as a length rather than a dimensionless ratio of two lengths.
Put it right by stressing that θ = s ÷ r has no unit other than rad.
Using degrees directly in a formula that requires radians, such as θ ≈ λ ÷ D.
Put it right by converting to radians before substitution.
Confusing the conversion factor by multiplying by 180 ÷ π when changing degrees to radians.
Put it right by remembering that a degree is smaller than a radian, so the number of radians is less than the number of degrees.
Exam tips
- Write the conversion factor explicitly before substituting numbers so the examiner can see your method.
- Check whether a formula expects radians or degrees, and convert first if necessary.
- Keep answers to three significant figures unless the question states otherwise, and include the unit rad where an angle is required.
Try the lesson
The start of the Advantages of large diameter telescopes (A-level only): Students should be familiar with the rad as the unit of angle. lesson, made from checked teaching notes for this specification point.
Have a go first
Which unit is used to measure an angle in the SI system?
Listen
The radian is the SI unit of angle and is essential in astronomy because it links an angle to the arc it subtends. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius, so θ = s ÷ r. A full circle is 2π rad, a straight line is π rad and a right angle is π ÷ 2 rad. Convert degrees to radians by multiplying by π ÷ 180, and radians to degrees by multiplying by 180 ÷ π. For example, 30° = 30 × π ÷ 180 = π ÷ 6 rad ≈ 0.524 rad. Radians are needed for the small-angle approximation θ ≈ λ ÷ D and for angular resolution, where θ must be in radians for the formula to work. A strong answer earns marks for these points. States that one radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. Uses θ = s ÷ r to relate arc length, radius and angle in radians. Converts between degrees and radians using π rad = 180°, multiplying by π ÷ 180 or 180 ÷ π as appropriate. Recognises that a full circle is 2π rad and that a right angle is π ÷ 2 rad. A common slip: Treating a radian as a length rather than a dimensionless ratio of two lengths. Instead, stressing that θ = s ÷ r has no unit other than rad. Exam tip: Write the conversion factor explicitly before substituting numbers so the examiner can see your method.
Key words
Say what each word means before you turn the card.
Radian
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Angular measure
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Conversion between degrees and radians
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Astronomical calculations
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See every definition
- Radian
- The angle subtended at the centre of a circle by an arc equal in length to the radius.
- Angular measure
- An angle linked to the arc it subtends, where a full circle is 2π rad and a right angle is π ÷ 2 rad.
- Conversion between degrees and radians
- Degrees are changed to radians by multiplying by π ÷ 180, and radians to degrees by multiplying by 180 ÷ π.
- Astronomical calculations
- Radian measure is applied in angular resolution and the small-angle approximation θ ≈ λ ÷ D, where θ must be in radians.
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