Home / Topics / Kinematics
Non-uniform circular motion
Advanced
Tangential acceleration changes speed while radial changes direction.
a = √(a_r²+a_t²)If the speed changes, there is a tangential acceleration at (changing speed) as well as the radial v²/r. The total acceleration is the vector sum with magnitude √(ar² + at²).
A car speeding up in a roundabout feels pushed both inward and forward.
Don't forget at when speed varies, like a pendulum swinging.
In more detail
In non-uniform circular motion, the speed changes as well as the direction. The acceleration then has a tangential part that changes speed and a radial part that changes direction.
Real-world uses
- A car speeding up on a curved road has both tangential and centripetal acceleration.
- Roller coaster designers check both components of acceleration at loops.
- A roller coaster that speeds up on a circular track has both a radial and a tangential acceleration, and the engineer must design for both.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is tangential acceleration?
The rate of change of speed, directed along the path.
Is the total acceleration towards the centre?
No. Only the radial component is towards the centre, and the tangential component is along the path.
Can the total acceleration point to the centre?
Not in general. When speed changes, the tangential part makes the total acceleration point between the tangent and the centre.
Related topics in Kinematics
Angular displacement and velocity · Period and frequency · Centripetal acceleration · Angular acceleration · Rotational kinematics equations · Motion in polar coordinates