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

Answer:

D. 247 m/s2

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

$\omega = \frac{\Delta \theta}{\Delta t}=\frac{20 \pi}{4.0 s}=15.7 rad/s$

And so, the centripetal acceleration is

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

Answer 2

4.00= 10 revolutions       

8sec= 20 revolutions

16sec= 30 revolutions

idk id say 247 m/s2