# Linear acceleration Formula

Before defining the linear or tangential acceleration it is necessary to first clarify that it is a term related to the circular movement; it describes a circular path around an axis on which it rotates maintaining a constant radius. When the speed of this movement is also maintained in time, what is known as uniform circular movement takes place. When a circular movement is made, the moving body has an angular velocity, since it rotates constantly with a certain inclination. The elements that compose its definition are the rotation angle for each time unit. Tangential velocity is the velocity presented by the body at a given moment in time, taking into account its direction and sense, as well as the radius by which it is traveling in a particular fraction of its trajectory. Tangential acceleration is the magnitude that links the variation of speed with time.

tangential acceleration = angular velocity / time * circle radius.

The equation is:

We have:

a_{t} = tangential acceleration.

= angular velocity

= time.

*r* = circle radius.

Linear acceleration Questions:

1)Calculate the linear acceleration of a circular path with radius 6 m that has an initial angular velocity of 6 rad/s and a final angular velocity of 9 rad/s whose variation was made in 15 seconds.

Answer: Let's calculate the variation of angular velocity in time, for that, we calculate first the variation of angular velocity and then we apply the equation of linear acceleration.

= 9rad/s - 6 rad/s = 3rad/s.

= 15 s.

*r* = 6 m

= (3 rad/s / 15 sec)* 6 m = 1.2 m/s^{2}

a_{t} = 1.2 m/s^{2}.

2)What is the final angular velocity of an object moving on a circular path of radius 10 m if its tangential acceleration is 2 m/s^{2} and part of rest in a time of 20 seconds?

Answer: Using the tangential acceleration equation we can determine the value of the final velocity.

a_{t} = ω * r / t →

ω = a_{t} * t/ r = (2 m/s^{2}*20 s) / 10 m = 4 rad / s

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