Instant Acceleration Center

Instantaneous center of acceleration - in the plane-parallel motion of an absolutely solid body, a point connected with this body and located in the plane of motion of the body, the acceleration of which at the given moment of time is equal to zero.

Construction of the instantaneous center of acceleration Q

The position of the instantaneous center of acceleration in the general case does not coincide with the position of the instantaneous center of velocities . However, in some cases, for example, with a purely rotational motion , the position of these two points may coincide.

Special cases of the position of the instantaneous acceleration center Q

In order to determine the position of the instantaneous center of acceleration, it is necessary to draw straight lines at equal angles to the acceleration vectors of two different points of the body $\gamma$ ${\ displaystyle \ gamma}$ $\ gamma$ . If the angular acceleration is positive, then the angle is delayed from the acceleration vector counterclockwise, otherwise - clockwise. At the intersection of the drawn lines and will be the instantaneous center of acceleration. Angle $\gamma$ ${\ displaystyle \ gamma}$ $\ gamma$ must satisfy the equality:

\operatorname {tg} \gamma ={\frac {\varepsilon }{\omega ^{2}}},

{\ displaystyle \ operatorname {tg} \ gamma = {\ frac {\ varepsilon} {\ omega ^ {2}}},}

{\ displaystyle \ operatorname {tg} \ gamma = {\ frac {\ varepsilon} {\ omega ^ {2}}},}

Where

\varepsilon

{\ displaystyle \ varepsilon}

\ varepsilon

- angular acceleration of the body;

\omega

{\ displaystyle \ omega}

\ omega

- the angular velocity of the body.

The magnitude of the acceleration of a point is proportional to its distance to the instantaneous center of acceleration

a_{A}=AQ{\sqrt {\omega ^{4}+\varepsilon ^{2}}},\ a_{B}=BQ{\sqrt {\omega ^{4}+\varepsilon ^{2}}}.

{\ displaystyle a_ {A} = AQ {\ sqrt {\ omega ^ {4} + \ varepsilon ^ {2}}}, \ a_ {B} = BQ {\ sqrt {\ omega ^ {4} + \ varepsilon ^ {2}}}.}

{\ displaystyle a_ {A} = AQ {\ sqrt {\ omega ^ {4} + \ varepsilon ^ {2}}}, \ a_ {B} = BQ {\ sqrt {\ omega ^ {4} + \ varepsilon ^ {2}}}.}

Literature

Targ S. M. A short course in theoretical mechanics. Textbook for technical colleges. - 10th ed., Rev. and add. - M .: Higher. school., 1986.— 416 s, ill.
Basic course in theoretical mechanics (part one) N. N. Buchholz, Nauka Publishing House, Main Edition of Physics and Mathematics, Moscow, 1972, 468 pp.
Zhukovsky N.E. Theoretical mechanics

Instant Acceleration Center

Literature

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