a. 7.0 m/s
First of all, we need to convert the angular speed (1200 rpm) from rpm to rad/s:
[tex]\omega = 1200 \frac{rev}{min} \cdot \frac{2\pi rad/rev}{60 s/min}=125.6 rad/s[/tex]
Now we know that the row is located 5.6 cm from the centre of the disc:
r = 5.6 cm = 0.056 m
So we can find the tangential speed of the row as the product between the angular speed and the distance of the row from the centre of the circle:
[tex]v=\omega r = (125.6 rad/s)(0.056 m)=7.0 m/s[/tex]
b. [tex]875 m/s^2[/tex]
The acceleration of the row of data (centripetal acceleration) is given by
[tex]a=\frac{v^2}{r}[/tex]
where we have
v = 7.0 m/s is the tangential speed
r = 0.056 m is the distance of the row from the centre of the trajectory
Substituting numbers into the formula, we find
[tex]a=\frac{(7.0 m/s)^2}{0.056 m}=875 m/s^2[/tex]
