Respuesta :
Answer:
P = 180 watts
Explanation:
It is given that,
Inertia of the wheel, [tex]I=16\ kgm^2[/tex]
Net torque acting on the wheel, [tex]\tau=24\ Nm[/tex]
Initial speed of the wheel, [tex]\omega_i=0[/tex]
Time, t = 5 s
We know that the relation between the torque and the angular acceleration is given by :
[tex]\tau=I\alpha[/tex]
[tex]\alpha[/tex] is the angular acceleration
[tex]\alpha =\dfrac{\tau}{I}[/tex]
[tex]\alpha =\dfrac{24\ Nm}{16\ kgm^2}[/tex]
[tex]\alpha =1.5\ rad/s^2[/tex]
Using first equation of rotational kinematics as :
[tex]\omega_f=\omega_i+\alpha t[/tex]
[tex]\omega_f=1.5\times 5[/tex]
[tex]\omega_f=7.5\ rad/s[/tex]
We know that the rate at which the work is done by the torque is called the power of any object. Its formula in rotational motion is given by :
[tex]P=\tau \times \omega_f[/tex]
[tex]P=24\ Nm\times 7.5\ rad/s[/tex]
P = 180 watts
So, the power of the wheel is 180 watts. Hence, this is the required solution.
