Question

5. Consider an object of mass m moving with constant speed v in a circle of radius r.

What is the algebraic expression for the centripetal acceleration a_c of the object in terms of its speed v and radius r? (Use any variable stated in this part.)

a_c =

Answer 1

When an object of mass m moving with constant speed v in a circle of radius r. Then the centripetal force acting on the object which keep the object on a circular path can be written as;

   $\small F=m\frac{v^{2}}{r}$

   $\small \Rightarrow ma_{c}=m\frac{v^{2}}{r}$

Here a_c is centripetal acceleration of the object. Therefore;

   $\small \Rightarrow a_{c}=\frac{v^{2}}{r}$