Question

If an object moves in uniform circular motion in a circle of radius R = 1.00 meter, and the object takes 4.00 seconds to complete ten revolutions, calculate the centripetal acceleration. a = _____ m/s2

A. 3.14 m/s2
B. 78.5 m/s2
C. 98.7 m/s2
D. 247 m/s2

Answer 1

4.00= 10 revolutions

8sec= 20 revolutions

16sec= 30 revolutions

idk id say 247 m/s2

Answer 2

D. 247 m/s2

Step-by-step explanation:

The centripetal acceleration is given by:

`a=\omega^2 r`

where

`\omega` is the angular speed

r = 1.00 m is the radius of the circular trajectory

The object takes 4.00 seconds to complete 10 revolutions. 1 revolution corresponds to an angle of
`2 \pi rad`, so 10 revolutions correspond to an angle of
`10 \cdot 2 \pi = 20 \pi rad`. The angular speed is therefore

`\omega = (\Delta \theta)/(\Delta t)=(20 \pi)/(4.0 s)=15.7 rad/s`

And so, the centripetal acceleration is

`a=\omega^2 r = (15.7 rad/s)^2 (1.0 m)=246.5 m/s^2 \sim 247 m/s^2`