Write the formulae for the centripetal force acting on a body performing circular motion and the
escape velocity of a body from the Earth surface.
Answers
Explanation:
What is a centripetal force?
A centripetal force is a net force that acts on an object to keep it moving along a circular path.
In our article on centripetal acceleration, we learned that any object traveling along a circular path of radius 'r' with velocity ‘v' experiences an acceleration directed toward the center of its path,
a = v²/r
However, we should discuss how the object came to be moving along the circular path in the first place. Newton’s 1ˢᵗ law tells us that an object will continue moving along a straight path unless acted on by an external force. The external force here is the centripetal force.
It is important to understand that the centripetal force is not a fundamental force, but just a label given to the net force which causes an object to move in a circular path. The tension force in the string of a swinging tethered ball and the gravitational force keeping a satellite in orbit are both examples of centripetal forces. Multiple individual forces can even be involved as long as they add up (by vector addition) to give a net force towards the center of the circular path.
Starting with Newton's 2ⁿᵈ law :
a = f/m
and then equating this to the centripetal acceleration,
v²/r = F/m
We can show that the centripetal force Fc has magnitude
Fc = mv²/r
and is always directed towards the center of the circular path. Equivalently, if \omegaωomega is the angular velocity then because v = rw,
Fc = mrw²
In our article on centripetal acceleration, we learned that any object traveling along a circular path of radius r with velocity v experiences an acceleration directed toward the center of its path, a = v 2 r a = \frac{v^2}{r} a=rv2a, equals, start fraction, v, squared, divided by, r, end fraction.
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