Question

How can I calculate the rotation of the acceleration vector of a circular motion where the tangencial motion is constant?

Answer 1

Answer on Question #54200, Physics-Mechanics-Kinematics-Dynamics

How can I calculate the rotational acceleration vector of a circular motion where the tangential motion is constant?

Answer

The acceleration vector of a circular motion is

$$\ddot {a} = \frac {d v}{d t} \vec {e _ {t}} + \frac {v ^ {2}}{r} \vec {e _ {n}},$$

where $\vec{e_t}$ is a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time, $\vec{e_n}$ is a normal unit vector.

When the tangential motion is constant

$$\frac {d v}{d t} = 0 \rightarrow \ddot {a} = \frac {v ^ {2}}{r} \vec {e _ {n}}.$$