Answer:
\(a_c=246.5 \frac{m}{s^2}\)
Explanation:
The formula for centripetal acceleration is:
\(a_c=rw^2\)
Where,
\(r:\) radius.
\(w:\)Angular speed.
Angular speed is defined by:
\(w=\frac{\Delta\theta}{\Delta t}\)
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:
\(w=\frac{\Delta\theta}{\Delta t}\\\\w=\frac{20\pi rad}{4.0s}\)
\(w=5\pi \frac{rad}{s}\\w=15.7\frac{rad}{s}\)
Now we have,
\(a_c=rw^2\\a_c=r(15.7\frac{rad}{s})^2\)
r=1.0m
\(a_c=1.0m(15.7\frac{rad}{s})^2\\\\a_c=1.0(246.5)\frac{m}{s^2} \\\\a_c=246.5\frac{m}{s^2}\)
Then the centripetal acceleration is:
\(a_c=246.5 \frac{m}{s^2}\)
