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Angular kinematics review

Overview of equations and skills for angular kinematics, including how to choose the best angular kinematics formula.


  1. ω=ω0+αt
  2. θ=θ0+ω0t+12αt2
  3. ω2=ω02+2α(θθ0)
  4. θθ0=12(ω0+ω)t
  • θ0 is initial angle
  • θ is final angle
  • t is the
  • ω0 is initial angular velocity
  • ω is final angular velocity
  • α is angular acceleration
  • Angular acceleration α is constant over the time interval.

Choosing the best rotational kinematic formula

To choose the rotational kinematic formula that's right for your problem, figure out which rotation variable you are not given and not asked to find. For example, we could use equation 1, ω=ω0+αt, to solve for the variables ω, ω0, α, or t if we knew the values of the other three variables.
Note that each kinematic formula is missing one of the five kinematic variables.

Common mistakes and misconceptions

People forget that all the rotational kinematic variables — θ0,θ,ωo,ω,α — are vectors and commonly have negative signs. A missing negative sign is a very common source of error. For example, a wheel’s rotation slows down if its angular velocity is counterclockwise (positive direction) and its angular acceleration is clockwise (negative direction). Slowing down is only possible if the angular velocity and acceleration have opposite signs.

Learn more

For deeper explanations of rotational kinematics, see our video about rotational kinematics.
To check your understanding and work toward mastering these concepts, check out the exercises in this tutorial.

Want to join the conversation?

  • mr pants purple style avatar for user huseynmlk7
    I do not understand that why our speed or acceleration is negative when the object is moving clockwise or virce versa
    (7 votes)
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    • blobby green style avatar for user Shobhit Maheshwari
      Its also due to the fact that the speed(velocity to be precise) and acceleration are vectors and hence the direction in which they are applied matters to us. Since we are working in a rotating system, clockwise being negative and counter-clockwise being positive is analogous to moving forward being positive and moving backward being negative in a translational system
      (7 votes)
  • leafers sapling style avatar for user Yummypum
    what if you don't know what the initial angular velocity is? all four formulas listed above seem to include it.
    (2 votes)
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  • blobby green style avatar for user Tanaya Dalvi
    A fan is rotating at 90rpm. It is then switched off. It stops after 21 revolutions.Calculate the time taken by it to stop assuming that the friction torque is constant.....why is time 2x theta in the solution
    (1 vote)
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  • blobby green style avatar for user Phil Smith
    Why do you guys intersperse your terms? It is very confusing! Also there is no way I can follow you when you rearrange the equation in such non-descript fashions. How the hell are we supposed to learn when you jack us around like this? It makes this an exercise in futility!
    (1 vote)
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