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Radial acceleration is used when calculating the total force. Tangential acceleration is not used in calculating total force because it is not responsible for keeping the object in a circular path. The only acceleration responsible for keeping an object moving in a circle is the radial acceleration.
are called the tangential acceleration and the normal or radial acceleration (or centripetal acceleration in circular motion, see also circular motion and centripetal force), respectively. Geometrical analysis of three-dimensional space curves, which explains tangent, (principal) normal and binormal, is described by the Frenet–Serret formulas ...
which breaks into the radial acceleration d 2 r / dt 2 , centripetal acceleration –rω 2, Coriolis acceleration 2ω dr / dt , and angular acceleration rα. Special cases of motion described by these equations are summarized qualitatively in the table below.
The first "centrifugal acceleration" term depends only on the radial position r and not the velocity of our object, the second "Coriolis acceleration" term depends only on the object's velocity in the rotating frame v rot but not its position, and the third "Euler acceleration" term depends only on position and the rate of change of the frame's ...
The negative sign shows that the acceleration is pointed towards the center of the circle (opposite the radius), hence it is called "centripetal" (i.e. "center-seeking"). While objects naturally follow a straight path (due to inertia), this centripetal acceleration describes the circular motion path caused by a centripetal force.
The radial acceleration (perpendicular to direction of motion) is given by = =. It is directed towards the center of the rotational motion, and is often called the centripetal acceleration . The angular acceleration is caused by the torque , which can have a positive or negative value in accordance with the convention of positive and negative ...
In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration [8] or transverse acceleration [9] is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axis. This article ...
Newton's law of motion for a particle of mass m written in vector form is: = , where F is the vector sum of the physical forces applied to the particle and a is the absolute acceleration (that is, acceleration in an inertial frame) of the particle, given by: = , where r is the position vector of the particle (not to be confused with radius, as ...