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Show that centripetal force is also shown by ch5para9

ANSWER

Centripetal force is the one that compels the body to move in the circle. Mathematically, it is given by the Newton’s Second Law of motion by putting  , where ac  represents the centripetal acceleration.

fc in vector form

Please note that the minus sign indicates that the force is center-seeking whereas radius   is directed away from the center.
Now let’s multiply RHS by 1 = r/r,

ch5para10

Since rdotr therefore,

ch5para11

Similarly  v/r = ω , therefore, the above equation becomes,ch5para12

From equations (1), (3) and (2)

This proves the result.

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