A child sitting 1.08 m from the center of a merry-go-round moves with a speed of 1.20 m/s.
(a) Calculate the centripetal acceleration of the child.
radius is zero? then zero centripetal acceleration
centripetal acceleration= radius*angularVelocity^2
To calculate the centripetal acceleration of the child, we can use the equation:
\(a = \frac{{v^2}}{{r}}\)
Where:
- \(a\) is the centripetal acceleration.
- \(v\) is the velocity of the child.
- \(r\) is the radius of the circular path.
In this case, the velocity of the child is given as 1.20 m/s, and the child is sitting 1.08 m from the center of the merry-go-round.
Now, we can substitute the given values into the equation and solve for \(a\):
\(a = \frac{{(1.20)^2}}{{1.08}}\)
\(a = \frac{{1.44}}{{1.08}}\)
\(a = 1.33 \, \text{m/s}^2\)
Therefore, the centripetal acceleration of the child is 1.33 m/s².