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Consider a stone tied to a string and held by your hand. If you rotate by holding it firmly with your hand, the stone moves in a circular path, with a radius equal to the length of the string. The string held firmly by your hand exerts a force on the stone, which is termed as Centripetal Force.
As per the Newton’s second law, every object experiences an acceleration that is in the direction of the force acting on it. Here, the force is acting towards the center. Hence, the stone experiences an acceleration, termed as Centripetal acceleration, directed towards the center - which is your hand,.
Centripetal acceleration is an acceleration a body moving in circular path experiences due to the centripetal force.
If you leave the stone suddenly when it is moving in the circular path, it moves along the straight line that is tangential to that point at that instant. The velocity with which it leaves the circular path is called Tangential velocity ‘v’.
An object moving in circular path experiences three types of accelerations:
While angular acceleration is an angular quantity, the rest two are linear quantities.
For a body of mass ‘m’ moving in a circle of radius ‘r’ with a tangential velocity ‘v’, the centripetal acceleration is given by: ac = v2 / r
In terms of linear velocity, you can calculate the centripetal acceleration as ac= ω2r, as we know that v=rω
The centripetal acceleration is also defined as the rate of change of tangential velocity: ac= Lim(Δv→0)[(Δvt/Δt)]
Note: An object moving in a circular path can have zero tangential acceleration, but never zero centripetal acceleration. If the body is having zero tangential acceleration, it means it is moving with constant angular velocity and that the angular acceleration is also zero.
But if a body moving in a circular path has zero centripetal acceleration, it means that its tangential velocity is not changing, which implies it is not moving in a circular at all.
The moon gravitates towards the earth and by the force of gravity is continually drawn off from a rectilinear motion and retained in its orbit.
- Isaac Newton
A device called Centrifuge works on the principle of centripetal acceleration. A centrifuge is a device that is used in labs and industries to separate particles of varying densities, mostly from liquids.
The centrifuge the container containing the liquid in rotation with high speed and applies a perpendicular force to the axis of the spin. As a result, the denser particles move outwards, while the lighter particles move towards the center.
This principle of centrifuge is commonly used in the following industries:
Do you know?
To test the tolerance levels of astronauts, human centrifuges are designed with extremely large values of accelerations, that are often many times higher than the Earth’s gravity.
Human centrifuges, extremely large centrifuges, have been used to test the tolerance of astronauts to the effects of accelerations larger than that of Earth’s gravity.
Using CalculatorHut’s online free centripetal acceleration calculator, you can calculate any parameter related to the centripetal acceleration - radius, velocity, and centripetal acceleration. It is a very handy tool for students to check if their calculations are correct.
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