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Further Mechanics

The radian, angular displacement and angular velocity

  • 2 things to know
  • Papers 1 and 3

Overview

Recall questions on the definition of the radian, converting between degrees and radians, the arc-length relationship, and the definitions of angular displacement and velocity.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

What is the relationship between arc length, radius and angle, and why must the angle be in radians?

Numbers

What are angular displacement and angular velocity, and what is the unit of angular velocity?

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 whose length is equal to the radius of that circle.

  2. 2

    How many radians are there in one complete revolution?

    Model answer

    There are 2π radians in a full revolution, which is about 6.28 rad.

  3. 3

    How do you convert an angle from degrees into radians?

    Model answer

    Multiply the angle in degrees by π/180, because 180° is equal to π rad.

  4. 4

    What is 45° expressed in radians?

    Model answer

    45 × π/180 = π/4 rad, which is 0.785 rad to 3 significant figures.

  5. 5

    What is 2.0 rad expressed in degrees?

    Model answer

    2.0 × 180/π = 115° to 3 significant figures.

  6. 6

    State the relationship between arc length, radius and angle:

    Model answer

    The arc length is given by s = rθ, where θ is the angle at the centre measured in radians.

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