A particle rotates in a circle with centripetal acceleration a = 14 m/s^2 .

Question

A particle rotates in a circle with centripetal acceleration a = 14 m/s^2 .

What is a if the radius is doubled without changing the particle's speed?

What is a if the speed is doubled without changing the circle's radius?

Answer 1

a = v²/r

If radius is doubled without changing speed then a = 7m/s².

If speed is doubled without changing radius then a = 56 m/s²

Answer 2

We have that the equation for centripetal acceleration a = (mv^2)/r. If we double the radius r, then a will decrease by a factor of 2, so a = 7 m/s^2. If we double the speed v, then a will increase by a factor of 4, so a = 56 m/s^2.