Answer: 5.8 s
Explanation:
Newton's second law for rotational motions states that:
[tex]\tau=I \alpha[/tex]
where
[tex]\tau[/tex] is the net torque
I is the moment of inertia
[tex]\alpha[/tex] is the angular acceleration
Substituting data and re-arranging the equation, we find the angular acceleration:
[tex]\alpha=\frac{\tau}{I}=\frac{66 Nm}{175 kg m^2}=0.38 rad/s^2[/tex]
Now we can use the SUVAT equation for rotational motions:
[tex]\theta(t)=\frac{1}{2}\alpha t^2[/tex]
where
[tex]\theta(t)=2 \pi[/tex] is the angle corresponding to one revolution
t is the time taken
Re-arranging the equation:
[tex]t=\sqrt{\frac{2 \theta}{\alpha}}=\sqrt{\frac{2(2\pi)}{0.38 rad/s^2}}=5.8 s[/tex]
During the rotational motion, the wheel makes a complete rotation in either direction depending on the direction of torque. The wheel will take 5.8 seconds to make one complete revolution, after starting from rest.
The magnitude of the force acting on an object during the rotational motion is known as torque. Mathematically, the torque is given as the product of the radial distance from the axis and the linear force along the axis.
Given data -
The magnitude of torque is, T = 66 N-m.
The moment of inertia is, [tex]I = 175 \;\rm kg.m^{2}[/tex].
Let us first calculate the angular acceleration by using the formula,
[tex]T = I \times \alpha[/tex]
Here, [tex]\alpha[/tex] is the angular acceleration. Solving as,
[tex]66 = 175 \times \alpha\\\\\alpha = 0.38 \;\rm rad/s^{2}[/tex]
Now, using the second rotational equation of motion as,
[tex]\theta = \omega_{0}t+\dfrac{1}{2} \alpha t^{2}[/tex]
Here, [tex]\theta[/tex] is the angular displacement and for a complete rotation, its value is [tex]2 \pi[/tex].
Solving as,
[tex]2 \pi = (0)t+\dfrac{1}{2} \times 0.38 \times t^{2}\\\\t=\sqrt{\dfrac{2 \times 2 \pi}{0.38}}\\\\t = 5.8 \;\rm s[/tex]
Thus, we can conclude that the wheel will take 5.8 seconds to make one complete revolution, after starting from rest.
Learn more about the torque here:
https://brainly.com/question/3388202
