Explanation:
We have equation of motion v = u + at
Initial angular velocity, u = 0 rad/s
Final angular velocity, v = 32 rad/s
Time, t = 0.40 s
Substituting
v = u + at
32 = 0 + a x 0.40
a = 80 rad/s²
Angular acceleration is 80 rad/s²
We have equation of motion s = ut + 0.5 at²
Initial angular velocity, u = 0 rad/s
Angular acceleration, a = 80 rad/s²
Time, t = 0.4 s
Substituting
s = ut + 0.5 at²
s = 0 x 0.4 + 0.5 x 80 x 0.4²
s = 6.4 rad
Angular displacement = 6.4 rad
[tex]\texttt{Number of revolutions = }\frac{6.4}{2\pi}=1.02[/tex]
Number of revolutions undergone is 1.02
This question involves the concepts of the equations of motion for angular motion.
a) The angular acceleration will be "80 rad/s²".
b) It goes through "1.02 revolutions" in the process.
a)
We will use the first equation of motion for angular motion to find out the angular acceleration:
[tex]\alpha=\frac{\omega_f-\omega_i}{t}[/tex]
where,
[tex]\alpha[/tex] = angular acceleration = ?
[tex]\omega_f[/tex] = final angular speed = 32 rad/s
[tex]\omega_i[/tex] = initial angular speed = 0 rad/s
t = time taken = 0.4 s
Therefore,
[tex]\alpha =\frac{32\ rad/s-0\ rad/s}{0.4\ s}\\\\\alpha= 80\ rad/s^2[/tex]
b)
Now, we will use the second equation of motion for the angular motion to find out the no. of revolutions:
[tex]\theta=\omega_it+\frac{1}{2}\alpha t^2[/tex]
where,
θ = angualr displacement = ?
Therefore,
[tex]\theta=(0\ rad/s)(0.4\ s)+\frac{1}{2}(80\ rad/s^2)(0.4\ s)^2\\\\\theta=6.4\ rad[/tex]
Now, the number of revolutions (N) are given as follows:
[tex]N=\theta(\frac{1\ rev}{2\pi\ rad})\\\\N=(6.4\ rad)(\frac{1\ rev}{2\pi\ rad})\\\\[/tex]
N = 1.02 revolutions
Learn more about the angular motion here:
brainly.com/question/14979994?referrer=searchResults
The attached picture shows the angular equations of motion.
