uniform circular motion
Uniform Circular Motion
Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. In all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well. The animation at the right depicts this by means of a vector arrow.
An object moving in a circle is accelerating. Accelerating objects are objects which are changing their velocity - either the speed (i.e., magnitude of the velocity vector) or the direction. An object undergoing uniform circular motion is moving with constant speed; nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards. The animation at the right depicts this by means of a vector arrow.
The final motion characteristic for an object undergoing uniform circular motion is the net force. The net force acting upon such an object is directed towards the center of the circle; it is said to be an inward or centripetal force. Without such an inward force, an object would continue in a straight line, never deviating its direction. Yet, with the inward net force directed perpendicular to the velocity vector, the object is always changing its direction and undergoing an inward acceleration.
The same is true of a spacecraft in orbit around the Earth, or any object in circular motion - some force is needed to keep it there and that force is directed back towards the centre of the circle. In the case of the spacecraft, it is the gravitational attraction between the Earth and the spacecraft that acts to maintain the circular motion that is the orbit.
Satellites have to get up above the atmosphere and into the vacuum of space to orbit for any length of time. Roughly 320 km up is about the minimum to avoid atmospheric interference. The Hubble space telescope orbits at an altitude of 600 km or so. But the principle is exactly the same. The speed of the satellite is adjusted so that it falls to earth at the same rate that the curve of the earth falls away from the satellite. The satellite is perpetually falling, but it never hits the ground!
The force required to maintain the circular motion, known as centripetal force, can be determined using the following equation:
where
F = force in newtons (N)
m = mass in kilgrams (kg)
v = velocity in metres per second (ms^{-1})
r = distance to centre of circle or radius in metres (m)
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download worksheet 8.4.2.F - circular motion
download experiment 5 - circular motion |