Mechanics: Chapter 11 – Relative Velocity and Acceleration

If two reference frames A and B are different from each other only because they are moving at different constant velocities relative to each other, we can convert the displacements, velocities and accelerations with respect to A to the displacements, velocities and accelerations with respect to B using Galilean Transformation.

If at time t = 0, the origins of both A and B coincide, and B is moving at a constant velocity v_{0} with respect to A, then the displacement with respect to B, r_{B} can be calculated from the displacement with respect to A, r_{A} at time t using:

  • r_{B} = r_{A} - v_{0}t

Differentiating this with respect to time, we get,

  • v_{B} = v_{A} - v_{0}

and taking the second derivative, we get

  • a_{B} = a_{A}

Interestingly, acceleration remains the same in reference frames that can be transformed using Galilean transformation.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s