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### Course: Mechanics (Essentials) - Class 11th>Unit 12

Lesson 2: Motion with constant angular acceleration

# Angular kinematics review

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

## Equations

1. $\omega ={\omega }_{0}+\alpha t$
2. $\theta ={\theta }_{0}+{\omega }_{0}t+\frac{1}{2}\alpha {t}^{2}$
3. ${\omega }^{2}={\omega }_{0}^{2}+2\alpha \left(\theta -{\theta }_{0}\right)$
4. $\theta -{\theta }_{0}=\frac{1}{2}\left({\omega }_{0}+\omega \right)t$
Where:
• ${\theta }_{0}$ is initial angle
• $\theta$ is final angle
• $t$ is the
• ${\omega }_{0}$ 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, $\omega ={\omega }_{0}+\alpha t$, to solve for the variables $\omega$, ${\omega }_{0}$, $\alpha$, 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 — ${\theta }_{0},\theta ,{\omega }_{o},\omega ,\alpha$ — 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.

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?

• I do not understand that why our speed or acceleration is negative when the object is moving clockwise or virce versa
• 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