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Speed in a circle calculator

A-level Motion

Links the speed along the circle to the angular speed and the radius.

v = ω r

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

4.20 m/s

Working

  1. Write the equation
    v = ω r
  2. Substitute the values
    v = 12 × 0.35
  3. Calculate
    v = 4.2 m/s
  4. Give the answer to 3 significant figures
    v = 4.20 m/s

Worked example

Find v, the linear speed. Given: angular speed ω = 12.0 rad/s; radius r = 0.350 m.

  1. Write the equation
    v = ω r
  2. Substitute the values
    v = 12 × 0.35
  3. Calculate
    v = 4.2 m/s
  4. Give the answer to 3 significant figures
    v = 4.20 m/s

Symbols and units

SymbolQuantitySI unit
vLinear speedm/s
ωAngular speedrad/s
rRadiusm

Speed in a circle: rearranged

  • To find linear speed: v = ω r
  • To find angular speed: ω = v / r
  • To find radius: r = v / ω

Exam tip

ω must be in rad/s. Convert revolutions per minute before you use this equation.

Common questions

What is the formula for speed in a circle?

The equation is v = ω r, where v is the linear speed (m/s); ω is the angular speed (rad/s); r is the radius (m).

What units should I use for speed in a circle?

In SI units: linear speed in m/s, angular speed in rad/s, radius in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange v = ω r?

Rearranging gives these forms: to find linear speed: v = ω r. to find angular speed: ω = v / r. to find radius: r = v / ω.

Practise speed in a circle questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

More motion equations: Speed, distance and time, Acceleration, Final velocity, Velocity squared, Displacement under constant acceleration, Displacement from average velocity, Momentum, Force and change in momentum. See the full list on the a-level physics equation calculator page.