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Angular kinematics review

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

Equations

  1. omega, equals, omega, start subscript, 0, end subscript, plus, alpha, t
  2. theta, equals, theta, start subscript, 0, end subscript, plus, omega, start subscript, 0, end subscript, t, plus, start fraction, 1, divided by, 2, end fraction, alpha, t, squared
  3. omega, squared, equals, omega, start subscript, 0, end subscript, squared, plus, 2, alpha, left parenthesis, theta, minus, theta, start subscript, 0, end subscript, right parenthesis
  4. theta, minus, theta, start subscript, 0, end subscript, equals, start fraction, 1, divided by, 2, end fraction, left parenthesis, omega, start subscript, 0, end subscript, plus, omega, right parenthesis, t
Where:
  • theta, start subscript, 0, end subscript is initial angle
  • theta is final angle
  • t is the
  • omega, start subscript, 0, end subscript is initial angular velocity
  • omega is final angular velocity
  • alpha is angular acceleration
Assumption:
  • Angular acceleration alpha 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, omega, equals, omega, start subscript, 0, end subscript, plus, alpha, t, to solve for the variables omega, omega, start subscript, 0, end subscript, alpha, 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 — theta, start subscript, 0, end subscript, comma, theta, comma, omega, start subscript, o, end subscript, comma, omega, comma, alpha — 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.

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