levo

Circular Motion

The radian as a measure of angle

  • 3 things to know
  • Component 1

Overview

Recall questions on the definition of the radian in terms of arc and radius, converting between radians and degrees, why the radian is dimensionless, the number of radians in a full turn, and where the small angle approximation applies.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

State the equation linking arc length, radius and angle in radians, defining every symbol.

Numbers

How many radians are there in a complete circle?

Numbers

An angle of π/4 rad is subtended at the centre of a circle of radius 1.20 m. Calculate the arc length.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define the radian.

    Model answer

    One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of that circle.

  2. 2

    How many radians are there in a complete circle?

    Model answer

    A complete circle contains 2π radians, since the circumference is 2π times the radius.

  3. 3

    Convert one radian into degrees.

    Model answer

    One radian is 360/(2π) = 57.3°. Multiplying 57.3° by 2π returns 360°.

  4. 4

    Why is the radian described as a dimensionless unit?

    Model answer

    The radian is the ratio of an arc length to a radius, and dividing a length by a length leaves a pure number with no units.

  5. 5

    State the equation linking arc length, radius and angle in radians, defining every symbol.

    Model answer

    The equation is s = rθ, where s is the arc length in m, r is the radius in m and θ is the angle in rad.

  6. 6

    Calculate the arc length subtended by an angle of 1.20 rad on a circle of radius 0.250 m.

    Model answer

    The arc length is 0.250 × 1.20 = 0.300 m. Dividing 0.300 m by 0.250 m returns 1.20 rad.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Basic Physics
Kinematics
Dynamics
Energy Concepts

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The wires .
attractrepeltwist

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe equation is pV = NkT.
BThe pressure, p, is in Pa.
CThe volume V is in m³.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

The joule is a unit of energy.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Circular Motion, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.