Question

If an object moves in uniform circular motion in a circle of radius R = 2.00 meters, and the object takes 5.00 seconds to complete ten revolutions, calculate the centripetal acceleration.

Answer 1

Hi!

The linear velocity is given by:
v = ωR

And ω is given by: ω = 2π/T (where T is the time for 1 revolution)

Now, put these equations together:
v = 2πR/T

If it takes 5 seconds for 10 revolutions, then it takes 5/10 = 0.5 seconds for each revolution.

V = (2π * 2)/0.5
V = 4π/0.5
V = 8π rad/s

Then, we goes to the centripetal acceleration:
a = V²/R
a = 64π²/2
a = 32π² rad/s²

;)

Answer 2

`a=315.75\ m/s^2.`

Step-by-step explanation:

Time taken to complete 10 revoution,
`t=5.0 \ s.`

Radius,
`r=2.0\ m`.

We know,
`v=(2* \pi * r)/(T)`.

( T is time taken to complete one revolution).

`T=(5)/(10)=0.5 \ s`.

`v=(2* \pi* 2)/(0.5) \ m/s=25.13\ m/s.`

Centripetal acceleration,
`a=(v^2)/(r)`.

Therefore,
`a=(25.13^2)/(2)=315.75 \ m/s^2`.

Hence, it is the required solution.