Question

A particle rotates in a circle with centripetal acceleration a = 8.0 m/s² . What is 'a' if the speed is doubled without changing the circle's radius?

Answer 1

Given info : A particle rotates in a circle with centripetal acceleration, a = 8 m/s².

To find : the value of a if the speed is doubled without changing the circle's radius, is ..

solution : we know,

centripetal acceleration is the acceleration of a body  travelling in a circular path. it is given as , $a=\frac{v^2}{r}$

where v is linear speed of the particle and r is the radius of circular path.

here, speed of the particle is doubled without changing the radius of circle.

so, $a'=\frac{(2v)^2}{r}=4\frac{v^2}{r}=4a$

It is clear that the centripetal acceleration of the particle will be four times of its initial value. i.e., a' = 4 × 8 = 32 m/s²

therefore the centripetal acceleration of the particle will be 32 m/s².