Answer:
263.8 m/s2
Explanation:
Assume this is a solid disk, we can find its moments of inertia:
[tex]I = mr^2/2 = 3.8*1.6^2/2 = 4.864 kgm^2[/tex]
The torque T generated by force F = 18.4N is:
[tex]T = Fr = 18.4*1.6 = 29.44 Nm[/tex]
So the angular acceleration of the disk according to Newton's 2nd law is:
[tex]\alpha = T/I = 29.44 / 18.4 = 6.05 rad/s^2[/tex]
If the disk starts from rest, then after 3s its angular speed is
[tex]\omega = \alpha \Delta t = 6.05*3 = 18.16 rad/s[/tex]
And so its radial acceleration at this time and half way from the center to the edge is:
[tex]a_r = \omega^2(r/2) = 18.16^2*(1.6/2) = 263.8 m/s^2[/tex]
Note that this value is the same anywhere
