Tangential acceleration

The tangential (also path acceleration called) refers to the change in speed per time to the latter, undergoes a mass point on a curved path tangential. It is the product of the angular acceleration and the radius of curvature at the relevant point on the path. We consider here a circular path as an example.

If you only consider the amount of tangential acceleration, then:

${\displaystyle a_{\mathrm {T} }={\frac {\mathrm {d} v}{\mathrm {d} t}}={\frac {\mathrm {d} (\omega \cdot r)}{\mathrm {d} t}}=r\cdot {\frac {\mathrm {d} \omega }{\mathrm {d} t}}=r\cdot \alpha }$

Here, the amount of tangential acceleration, the web speed, the angular velocity, the radius of the circular path and the angular acceleration. ${\displaystyle a_{\mathrm {T} }}$ ${\displaystyle v}$ ${\displaystyle \omega }$ ${\displaystyle r}$ ${\displaystyle \alpha }$

The tangential acceleration is perpendicular to the centripetal acceleration , which is directed towards the center of the circle. The total acceleration is the sum of the vectors of tangential acceleration and centripetal acceleration.

The possibility of dividing the acceleration vector into tangential and normal acceleration was discovered for the first time by Huygens .

example

A merry-go-round begins to spin. So it experiences an angular acceleration . With the same angular acceleration, a person standing close to the axis of rotation experiences a lower tangential acceleration (small distance to the axis of rotation) than a person standing on the outer edge of the carousel (large distance to the axis of rotation). The tangential acceleration is proportional to the radius of the carousel: ${\displaystyle a_{\mathrm {T} }(t)}$ ${\displaystyle r}$

${\displaystyle a_{\mathrm {T} }=r\cdot \alpha (t)}$

Individual evidence

1. ↑ Carl Snell, Galileo Galilei: About Galilei as the founder of mechanical physics and about the method of the same . W. Ratz, University of Gent 1864 ( limited preview in the Google book search).