Answer:
[tex]a_c=246.5 \frac{m}{s^2}[/tex]
Explanation:
The formula for centripetal acceleration is:
[tex]a_c=rw^2[/tex]
Where,
[tex]r:[/tex] radius.
[tex]w:[/tex]Angular speed.
Angular speed is defined by:
[tex]w=\frac{\Delta\theta}{\Delta t}[/tex]
Where,
[tex]\theta:[/tex] position angle.
[tex]t:[/tex] time.
In this case we have that the object takes 4.0 seconds to complete ten revolutions.
You have to know that 1 revolution = [tex]2\pi rad[/tex], then
10 revolutions= [tex]10.2\pi rad = 20\pi rad[/tex]
Replacing
[tex]\Delta\theta=20\pi rad\\\Delta t=4.0s[/tex]
in the formula of Angular speed:
[tex]w=\frac{\Delta\theta}{\Delta t}\\\\w=\frac{20\pi rad}{4.0s}[/tex]
[tex]w=5\pi \frac{rad}{s}\\w=15.7\frac{rad}{s}[/tex]
Now we have,
[tex]a_c=rw^2\\a_c=r(15.7\frac{rad}{s})^2[/tex]
r=1.0m
[tex]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}[/tex]
Then the centripetal acceleration is:
[tex]a_c=246.5 \frac{m}{s^2}[/tex]
