Total acceleration

Definition

Total acceleration in uniform circular motion is the vector sum of the radial (centripetal) and tangential accelerations. It describes how both the speed and direction of an object change as it moves along a circular path.

5 Must Know Facts For Your Next Test

1. The radial acceleration points towards the center of the circle and is given by $a_r = \frac{v^2}{r}$, where $v$ is the tangential speed and $r$ is the radius of the circle.
2. Tangential acceleration occurs if there is a change in the magnitude of velocity, calculated as $a_t = \frac{d|v|}{dt}$.
3. In uniform circular motion, total acceleration is predominantly radial since tangential acceleration equals zero when speed is constant.
4. The magnitude of total acceleration can be found using vector addition: $a_{total} = \sqrt{a_r^2 + a_t^2}$.
5. Total acceleration explains both how quickly an object speeds up or slows down (tangential) and how its direction changes (radial).

Review Questions

• What are the components that make up total acceleration in circular motion?
• If an object moves with a constant speed in a circle, what happens to its tangential acceleration?
• How do you calculate radial acceleration for an object moving in a circular path?

Related terms

Radial Acceleration: The component of acceleration directed towards the center of the circular path, responsible for changing direction.

Tangential Acceleration: The component of acceleration tangent to the circular path, responsible for changing speed.

Centripetal Force: The net force causing centripetal (radial) acceleration, directed toward the center of rotation.