Answer to Question #68832 in Mechanics | Relativity for gabby

Question

The radius of the path of an object in uniform circular motion is halved. The centripetal acceleration needed if its speed remains the same is _____.

Answer 1

By the definition of the centripetal acceleration we have:
a_c=v^2/r,
here, v is the speed of the object, r is the radius of the path of an object in uniform circular motion.
Then, the radius of the path of an object in uniform circular motion is halved. The centripetal acceleration needed if its speed remains the same is twice as great as before:
a_c^'=v^2/(r/2)=2 v^2/r=2a_c.
Answer:
c) twice as great as before