Question

What is centripetal force ? Formulate an expression for a planet revolving around sun in circular motion irrespective of its time of revolution ? ​

Answer 1

Explanation:

A centripetal force is a net force that acts on an object to keep it moving along a circular path.

Starting with Newton's 2ⁿᵈ law :

a = \frac{F}{m}a=

m

F

a, equals, start fraction, F, divided by, m, end fraction

and then equating this to the centripetal acceleration,

\frac{v^2}{r} = \frac{F}{m}

r

v

2

=

m

F

start fraction, v, squared, divided by, r, end fraction, equals, start fraction, F, divided by, m, end fraction

We can show that the centripetal force F_cF

c

F, start subscript, c, end subscript has magnitude

F_c = \frac{mv^2}{r}F

c

=

r

mv²

F, start subscript, c, end subscript, equals, start fraction, m, v, squared, divided by, r, end fraction

and is always directed towards the center of the circular path. Equivalently, if \omegaωomega is the angular velocity then because v=r\omegav=rωv, equals, r, omega,

F_c = m r \omega^2F

c

=mrω²