Answer:
a = 0.27 rad/s^2
Explanation:
First we will find the time t using the next equation:
θ = [tex]\frac{1}{2}at^2[/tex]
where θ is the angle in radians and a is the angular aceleration. So:
0.4 = [tex]\frac{1}{2}(1.6)t^2[/tex]
Solving for t:
t = 0.707s
Second, with that time, we will find the angular velocity w using the next equation:
w = at
where a is the angular aceleration, so:
w = (1.6)(0.707s)
w = 1.1312 rad/s
Now, the radial aceleration [tex]a_r[/tex] is calcualted as:
[tex]a_r[/tex] = [tex]w^2r[/tex]
[tex]a_r[/tex] = [tex](1.1312)^2(0.13)[/tex]
[tex]a_r[/tex] = 0.166 rad/s^2
Additionally, the tangential aceleration [tex]a_t[/tex] is calculated as::
[tex]a_t = ar[/tex]
[tex]a_t = (1.6)(0.13)[/tex]
[tex]a_t = 0.208 rad/s^2[/tex]
Finally, by pythagoras theorem, we find the total linear acceleration as:
[tex]a = \sqrt{a_r^{2}+a_t^2 }[/tex]
[tex]a = \sqrt{(0.208)^2+(0.166)^2 }[/tex]
a = 0.27 rad/s^2
