Question

If an object moves in uniform circular motion in a circle of radius R = 1.0 meter, and the object takes 4.0 seconds to complete ten revolutions, calculate the centripetal acceleration.

Answer 1

a = ω²r

r = 1 m
ω = 2πf = 2π * 10 / 4 = π*5 s⁻¹

Answer 2

`a_c=246.5 (m)/(s^2)`

Step-by-step explanation:

The formula for centripetal acceleration is:

`a_c=rw^2`

Where,

`r:` radius.

`w:`Angular speed.

Angular speed is defined by:

`w=(\Delta\theta)/(\Delta t)`

Where,

`\theta:` position angle.

`t:` time.

In this case we have that the object takes 4.0 seconds to complete ten revolutions.

You have to know that 1 revolution =
`2\pi rad`, then

10 revolutions=
`10.2\pi rad = 20\pi rad`

Replacing

`\Delta\theta=20\pi rad\\\Delta t=4.0s`

in the formula of Angular speed:

`w=(\Delta\theta)/(\Delta t)\\\\w=(20\pi rad)/(4.0s)`

`w=5\pi (rad)/(s)\\w=15.7(rad)/(s)`

Now we have,

`a_c=rw^2\\a_c=r(15.7(rad)/(s))^2`

r=1.0m

`a_c=1.0m(15.7(rad)/(s))^2\\\\a_c=1.0(246.5)(m)/(s^2) \\\\a_c=246.5(m)/(s^2)`

Then the centripetal acceleration is:

`a_c=246.5 (m)/(s^2)`