Respuesta :
Answer:
Axis of rotation in case 2 produces the most torque than case 1
Explanation:
Moment of inertia is a quantity that determines the torque needed for a required angular acceleration about a rotational axis.
formula wise its mass multiplied by the square of distance of it from the axis of rotation.
⇒[tex]I=mr^{2}[/tex]
for n number of discreet bodies,[tex]I=\sum mr^{2}[/tex]
for a rigid body,[tex]I=\int\limits {\delta mr^{2}} \, dr[/tex]
And [tex]\tau=I\alpha[/tex]
where, [tex]\tau[/tex] is torque
[tex]I[/tex] is moment of inertia and
[tex]\alpha[/tex] is angular acceleration
Now coming to the problem,
Case 1(When the axis of rotation is halfway between the two masses):
[tex]I=5*2^{2}+7*2^{2}[/tex]
[tex]=20+28[/tex]
[tex]=48kgm^{2}[/tex]
Case 2(When the axis of rotation is 0.50 m to the left of the 7.0 kg weight):
[tex]I=5*3.5^{2}+7*0.5^{2}[/tex]
[tex]=61.25+1.75[/tex]
[tex]=63kgm^{2}[/tex]
From [tex]\tau=I\alpha[/tex] we know that [tex]\tau[/tex] is proportional to [tex]I[/tex] when angular acceleration is constant which means axis of rotation in case 2 produces the most torque than case 1 because moment of inertia in case 2 is more than that of case 1
