Respuesta :
Answer:
Therefore the constant angular acceleration of the wheel 12.43 rad /s².
Explanation:
[tex]\triangle \theta =\omega_{av}t=\frac{\omega_f+\omega_i}{2}t[/tex]
[tex]\Rightarrow \triangle \theta =\frac{\omega_f+\omega_i}{2}t[/tex]
[tex]\Rightarrow \frac{2\triangle \theta}{t} ={\omega_f+\omega_i}[/tex]
[tex]\Rightarrow {\omega_i= \frac{2\triangle \theta}{t} -\omega_f}[/tex]
and
[tex]\alpha =\frac{\omega_f-\omega_i}{t}[/tex]
[tex]\omega_i[/tex] = initial angular velocity
[tex]\omega_f[/tex] = final angular velocity
[tex]\theta[/tex] = displacement
[tex]\alpha[/tex] = angular acceleration
t = time
Here [tex]\triangle \theta[/tex] = 37.0 revolution [tex]=37 \times(2\pi)[/tex] rad [ since one revolution = [tex]2 \pi[/tex]]
t=2.92 s
Final angular velocity = [tex]\omega_f[/tex] = 97.8 rad/s
To find the angular velocity, first we need to find out the initial angular velocity [tex](\omega_i)[/tex].
[tex]{\omega_i= \frac{2\triangle \theta}{t} -\omega_f}[/tex]
[tex]=\frac{2\times2\pi \times 37.0}{2.92}-97.8[/tex]
= 61.50 rad /s
Then the angular velocity is
[tex]\alpha =\frac{\omega_f-\omega_i}{t}[/tex]
[tex]=\frac{97.8-61.50}{2.92}[/tex] rad /s²
=12.43 rad /s²
Therefore the constant angular acceleration of the wheel 12.43 rad /s².
