Expert reviewed • 04 March 2025 • 9 minute read
Uniform circular motion is a fundamental concept in physics that describes the motion of an object traveling in a circular path at a constant speed.
To understand and analyse uniform circular motion quantitatively, we need to familiarise ourselves with several important equations:
Tangential velocity is the linear speed of an object moving in a circular path. It is defined as the distance traveled along the circumference of the circle divided by the time taken for one complete revolution (period, T):
Where:
A satellite orbits Earth in a circular path with a radius of 6,700 km. If it completes one orbit in 90 minutes, what is its tangential velocity?
Angular velocity represents the rate of change of angular position. It can be defined in two ways:
Where:
The SI unit for angular velocity is radians per second (rad/s).
An important relationship between tangential velocity and angular velocity is:
A wheel with a radius of 0.3 m rotates at an angular velocity of 10 rad/s. Calculate its tangential velocity.
Centripetal acceleration is the acceleration directed towards the centre of the circular path. It is given by:
We can also express centripetal acceleration in terms of angular velocity:
A car travels around a circular track with a radius of 50 m at a constant speed of 20 m/s. Calculate its centripetal acceleration.
Centripetal force is the force required to keep an object in circular motion. It is given by:
Where is the mass of the object.
We can also express centripetal force in terms of angular velocity:
A 0.5 kg object is attached to a string and swung in a horizontal circle with a radius of 1 m. If the object makes 2 revolutions per second, calculate the centripetal force.
First, let's calculate the angular velocity:
Now we can use the equation :
When approaching problems involving uniform circular motion, consider the following steps:
A satellite orbits Earth at an altitude of 200 km above the surface. The radius of Earth is 6,370 km. If the satellite's orbital period is 90 minutes, calculate:
Now, calculate the tangential velocity: