Answer:
The value for A is A= 0.6
The angular acceleration is [tex]\alpha (t) = 2.4 \ t \ m/s^2[/tex]
Explanation:
From the question we are told that
The radius of the disk is [tex]r = 25.0 \ cm = 0.25 \ m[/tex]
The linear acceleration is [tex]a(t) = At[/tex]
At time [tex]t = 3 \ s[/tex]
[tex]a(3) = 1.80 \ m/s^2[/tex]
Generally angular acceleration is mathematically represented as
[tex]\alpha(t) = \frac{a(t)}{r}[/tex]
Now at t = 3 seconds
a(3) = A * 3
=> 1.80 = A * 3
=.> A = 0.6
So therefore
a(t) = 0.6 t
Now substituting this into formula for angular acceleration
[tex]\alpha (t) = \frac{0.6 t }{R}[/tex]
substituting for r
[tex]\alpha (t) = \frac{0.6 t }{0.25}[/tex]
[tex]\alpha (t) = 2.4 \ t \ m/s^2[/tex]
