# Clarification(tangential acceleration)

• negation
In summary, in rotational motion (circular uniform), the tangential acceleration is the change in speed, not the change in velocity.
negation
As has been, accceleration is always the derivative of velocity.
In rotational motion (circular uniform), however, the tangential acceleration is the change in speed rather than velocity. Why is this so?

For any points on a uniform circular disc, the tangential velocity is changing because direction is changing but the magnitude of the tangential velocity (AKA speed) is constant. Well, make sense, the quantity remains the same but the direction changes and always in a direction tangent to the centripetal acceleration.
Why then is tangential acceleration make in reference to the change in speed rather than with the change in velocity?

The tangential acceleration cannot change the direction of the trajectory, the normal acceleration cannot change the magnitude of the trajectory.
All the tangential acceleration does is change the magnitude of the velocity, a.k.a speed.

HomogenousCow said:
The tangential acceleration cannot change the direction of the trajectory, the normal acceleration cannot change the magnitude of the trajectory.
All the tangential acceleration does is change the magnitude of the velocity, a.k.a speed.

But hasn't it always been so that acceleration is associated with velocity rather than speed?

negation said:
But hasn't it always been so that acceleration is associated with velocity rather than speed?

The total acceleration is the derivative of velocity.
It's just that this total acceleration has no tangential component if the magnitude of the velocity is constant.

negation said:
As has been, accceleration is always the derivative of velocity.
In rotational motion (circular uniform), however, the tangential acceleration is the change in speed rather than velocity. Why is this so?

Usually you would talk about acceleration using cartesian coordinates -- x and y. But there is nothing magical about the choice of the x and y directions. Any pair of directions at 90 degree angles works just as well.

When you express acceleration as "tangential" and "radial", what you are doing, in essence, is adopting a coordinate system in which the x direction ("tangential") is [momentarily] lined up with the way the object is moving and the y direction ("radial") is [momentarily] on a line running from the chosen center point.

Caution: There some ambiguity here. Sometimes the object is not moving in a circular path around the chosen "center point". It might be traveling in an ellipse or a spiral. In such cases, one might be tempted to apply the term "tangential" to refer to the direction a circular path would take -- at right angles to the "radial" direction. Let us assume that our "tangential" is exactly lined up with the object's motion and that the "center point" that we are using is at right angles to that. [If the object is moving in a circular path around the chosen center point then both of these assumptions will automatically be fulfilled]

The x component of acceleration is always equal to the rate of change of the x component of velocity. But with this particular choice of coordinates, speed is identically equal to the x component of velocity. So tangential acceleration is the same as the rate of change of speed.

## 1) What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity, which is the velocity in the direction of motion. It is a measure of how quickly the magnitude and/or direction of an object's velocity is changing.

## 2) How is tangential acceleration different from centripetal acceleration?

Tangential acceleration and centripetal acceleration are related but different concepts. Tangential acceleration is the change in an object's tangential velocity, while centripetal acceleration is the acceleration towards the center of a circular path. In other words, tangential acceleration deals with the change in speed or direction of an object's motion, while centripetal acceleration deals with the change in direction towards the center of a circular path.

## 3) What factors determine the magnitude of tangential acceleration?

The magnitude of tangential acceleration is determined by the object's tangential velocity and the rate of change of that velocity. It is also influenced by external forces, such as friction or air resistance, that may act on the object and affect its speed or direction of motion.

## 4) How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula at = vt/t, where at is the tangential acceleration, vt is the tangential velocity, and t is the time interval. Alternatively, it can also be calculated using the derivative of the tangential velocity with respect to time, as in at = dvt/dt.

## 5) What are some real-life examples of tangential acceleration?

Some examples of tangential acceleration in everyday life include a car accelerating along a curved road, a planet orbiting around the sun, and a rollercoaster moving along a track. In all of these cases, the object's velocity is constantly changing in the direction of motion, resulting in tangential acceleration.

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