Show that centripetal force is also shown by ![ch5para9](https://mashalscienceacademy.com/wp-content/uploads/2018/10/ch5para9.png)
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](https://mashalscienceacademy.com/wp-content/uploads/2018/10/fc-in-vector-form.png)
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](https://mashalscienceacademy.com/wp-content/uploads/2018/10/ch5para10.png)
Since
therefore,
![ch5para11](https://mashalscienceacademy.com/wp-content/uploads/2018/10/ch5para11.png)
Similarly v/r = ω , therefore, the above equation becomes,![ch5para12](https://mashalscienceacademy.com/wp-content/uploads/2018/10/ch5para12.png)
From equations (1), (3) and (2)
![](https://mashalscienceacademy.com/wp-content/uploads/2021/02/p11newc5e39.png)
This proves the result.
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