I don’t understand why tangential acceleration changes in value in a parabolic movement with constant acceleration (gravitational acceleration). Since acceleration is constant, tangential and centripetal acceleration are either both constant or one increases and other decreases in value. I was told that they both change in such movements but I don’t understand why since Tangential Acceleration is the derivative of the velocity value. Isn’t velocity supposed to change at the same rate in this case? And, since it changes, in which point of the trajectory is tangential acceleration at its maximum value?
[Physics] Why does tangential acceleration change in value
accelerationkinematicsvectors
Best Answer
In free fall without any horizontal motion, gravity changes the tangential velocity (as the path is vertical). The same applies to all situations unless the path is perpendicular to gravity.
This is illustrated in this post where tangential acceleration is
For example:
The velocity vector is tangent to the path
$$ \vec{v} = v\,\vec{e} $$
where $v$ is the speed
The acceleration (gravity) is decomposed into
$$ \vec{g} = \dot{v} \vec{e} + \frac{v^2}{r} \vec{n} $$
with $r$ the radius of curvature of the path.
with $$ \begin{aligned} \dot{v} & = \vec{e}\cdot \vec{g} \\ \frac{v^2}{r} & = \vec{n} \cdot \vec{g} \end{aligned} $$
Only if $\vec{e}\cdot\vec{g} = 0$ the tangential acceleration is zero (since the motion is perpendicular to gravity).