Respuesta :
Answer:
The no of revolutions is 2.032 revolution.
Explanation:
Given that,
Moment of inertia = 0.85 Kgm²
Radius = 170 mm
Force = 32 N
Time = 2s
We need to calculate the angular acceleration
Using formula of torque
[tex]\tau=I\times\alpha[/tex]
[tex]\alpha=\dfrac{\tau}{I}[/tex]
[tex]\alpha=\dfrac{F\times r}{I}[/tex]
Where, F = force
r = radius
I = moment of inertia
Put the value into the formula
[tex]\alpha=\dfrac{32\times170\times10^{-3}}{0.85}[/tex]
[tex]\alpha=6.4\ m/s^2[/tex]
We need to calculate the rotational speed
Using equation of angular motion
[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]
[tex]\omega_{f}=6.4\times2[/tex]
[tex]\omega=12.8\ rad/s[/tex]
We need to calculate the angular position
Using equation of angular motion
[tex]\theta=\omega_{i}+\dfrac{1}{2}\alpha t^2[/tex]
[tex]\theta=0+\dfrac{1}{2}\times6.4\times4[/tex]
[tex]\theta=12.8\ radian[/tex]
We need to calculate no of revolutions
[tex]n = \dfrac{\theta}{2\pi}[/tex]
[tex]n=\dfrac{12.8}{2\times3.15}[/tex]
[tex]n=2.032\ revolution[/tex]
Hence, The no of revolutions is 2.032 revolution.
