The Four Basic Equations in Kinematics (Rotational Motion)
Why is there always something wrong with my equations in Physics, Mechanics, or Kinematics? — Have you ever thought about this? Then this blog account is for you. It will explain — in detail — everything you are doing wrong. If you want to make sure you’re not doing any silly mistakes, follow me at MechanicallyChallenged on medium.com
The Stuff we already know
By now, you’ve probably already learned how to use the four basic kinematic’s formulas for linear motion. Like this when the acceleration is constant:
Or maybe, you’re a little more advanced and calculate for varying acceleration.
Seeing the connection
Dealing with rotational movement may be scary at first because there are all these new symbols. The secret is that we’ve already learned the formulas.
For constant acceleration, we have the equations depicted above. There is some change from linear motion, but the formulas are mostly the same. What’s different?
- Instead of
displacement \Delta x
, we now haveangular stretch \Delta \theta
What’s the difference? Displacement\Delta x
works in a straight line, while rotational motion\Delta \theta
works in an arc. - Instead of
linear velocity v
, we now haveangular velocity
. Angular velocity is the velocity an object has along an arc. The reason we don’t use linear velocity for objects going in circles is that the linear velocity for an object moving in an arc would be constantly changing direction.
A step further (When acceleration varies)
Let’s say we’re given a problem where the acceleration varies. Then the formulas in the last picture won’t work. What can we do? — Well, we already know how to deal with varying acceleration in linear motion, so let’s see if we can make another connection.
We can take the basic kinematics function equations and replace displacement with angular stretch, and linear velocity with angular velocity. This gives us three new equations we can use for rotational motion when the acceleration is not constant.
If you’ve discovered that we are now down on three formulas instead of four, there is a good reason for that. The missing formula is not dependent on acceleration.
Converting between the two systems
What do you do when you have either linear values or rotational values and want to convert them?
By manipulating the formula above, we can easily change between linear velocity and angular velocity after our desire. If you want a thorough explanation of how this formula is made, the following video is one of many that explains it well:
For more tips and tricks that will make you a Physics Master, watch out for more content from MechanicallyChallenged.