Circular Motion

When an object moves in circular path, it is called circular motion. If the speed of the object in circular motion remains constant, then it is called uniform circular motion. If the speed is not constant, then the motion is non-uniform circular motion. In circular motion, an acceleration acts on the body, whose direction is always towards the centre of the path. This acceleration is called centripetal acceleration or radial acceleration. Further, the Centripetal force is the force which makes the body to move in a circular path. Centripetal force is the force that is directed toward the center of an orbital path/spinning object which keeps the revolving object in its orbit. This is in opposition to the “centrifugal force” – a kind of fictitious force that appears to try to pull the object away from the center of the orbit (due to inertia).

Important Observations on Circular Motion

Artificial Satellites

An artificial satellite orbiting around the earth does not fall down. This is so because the attraction of earth provides the necessary acceleration for its motion. This acceleration is “constant” in magnitude but “changing in direction”. By the launch rocket, immediately before the satellite is established in the predetermined orbit, the speed given to it is 30, 000 km/hr. The speed must be great enough so gravity doesn’t bring the satellite back to Earth, but not so great that the satellite escapes gravity out into space. This means that the speed, which is provided by the rocket is the source of the centrifugal force, and the attraction of the earth holds it from moving away from this centrifugal force.

Working of Washing Machines

Both Centripetal Force and Centrifugal Force play role in working of a Washing Machine.

The spin dryer of a washing machine removes excess water from the clothing by rotating at a high speed. The high speed of rotation creates a high centrifugal force for the water in the clothing which causes it to be pulled to the outside of the spinning portion of the washing machine and away from the clothes. However, it is the Centripetal force that keeps the clothes themselves away from the outer portion of the washing machine. This is provided by the walls of the rotating spin dryer. Since there is insufficient centripetal force affecting the water (only friction & surface tension holding it to the clothes), it flows to the outer walls and is separated from the clothes, which removes the excess water.

Vehicles

Wheel of an automobile spins in mud because the centripetal force is not enough to hold the mud on tyre. When vehicles turn around at a turn, the centripetal force is provided by the friction between tyres and road.

The less desirable case of lack of centripetal force is when the rear wheel of an automobile spins in mud. The adhesion of the mud to the wheel which is the centripetal force in this case is not enough to hold the mud on the tyre. So it comes off tangentially to the tyre’s circular motion.

If a vehicle moves at very high speed over a curved path, the centrifugal force makes it topple. This is because the centrifugal force overcomes the frictional force between the road and the tyres of the vehicle. To prevent this, the curved tracks are always banked. It means that the outer edge of the road is slightly elevated at an angle. This angle of elevation is given by

Where g is acceleration due to gravity.

Due to banking of curves the centrifugal force balances with frictional force and equilibrium is reached. Thus toppling of vehicles is prevented on curved roads. This is known as banking of tracks. The racing track is designed like a concave disc for the same reason.

In circus there during the cage of death event, a motor cyclist drives a motor cycle at a high speed on the inner walls of a spherical cage of iron. But he does not fall off the motor cycle even when he is upside down. The centrifugal force keeps the motor cyclist glued to his seat while driving his motor cycle inside the cage.

Other Notes

• Total work done by the centripetal force is always zero because the centripetal force and displacement are at right angles to each other.
• During orbital motion of the planets, centripetal force is provided by the gravitational force between planet and sun.
• During orbital motion of electron around nucleus in an atom, the centripetal force is provided by Electrostatic force between electron and nucleus.
• When we swing a stone tied to a string, the centripetal force is provided by tension in the string.
• Centrifugal force is in opposite direction to Centripetal force. On earth, it is minimum at poles and maximum at equator.
• In centrifuges, heavier particles move away from the centre while lighter particles remain near axis of rotation.
• When a sample of blood is centrifuged, the red blood cells accumulate at the bottom, because red blood cells are heavier than White Blood Cells.
• Cream from milk is separated by centrifuges in dairy separators. Ultra centrifuges with speeds of the order of 5 x 10⁵ rpm are used to concentrate viruses in solution.
• Centrifuges are used in Uranium enrichment.
• Sugar crystals are separated from molasses with the help of a centrifuge. Honey is also separated from bees wax with the help of a centrifuge.