Respuesta :
Answer:
The moment of inertia is I = 0.126*R^2*M
Explanation:
We can calculate the moment of inertia of an object that starts from rest and has a final velocity using the energy conservation equation, as follows:
Ek1 + Ep1 = Ek2 + Ep2, where
Ek1 = kinetic energy of the object before to roll down
Ep1 = potential energy of the object
Ek2 = kinetic energy when the object comes down
Ep2 = potential energy of the object at the bottom
We have the follow:
Ek1 = 0
Ep1 = M*g*h
Ek2 = ((I*w)/2) + ((M*v^2)/2)
Ep2 = 0
Replacing values:
0 + M*g*h = ((I*w)/2) + ((M*v^2)/2) + 0
where:
M = mass of the object
g = gravitational acceleration
I = moment of the inertia
w = angular velocity = v/R
h = height
M*g*h = ((1/2) * I * (v^2/R^2)) + ((M*v^2)/2)
M*9.8*2 = (I*(5.9^2)/(2*R^2)) + ((5.9^2 * M)/2)
19.6 * M = ((17.4*I)/R^2) + 17.4*M
Clearing I, we have:
I = 0.126*R^2*M
When The moment of inertia is I = 0.126*R^2*M
What is Moment of Inertia?
Then We can calculate the moment of inertia of an object that starts from rest and also has a final velocity using the energy conservation equation, as follows:
Then Ek1 + Ep1 is = Ek2 + Ep2, where
After that Ek1 is = kinetic energy of the object before rolling down
Now Ep1 is = potential energy of the object
Then Ek2 is = kinetic energy when the object comes down
After that Ep2 is = potential energy of the object at the bottom
Now We have the follow is:
Then Ek1 = 0
Ep1 = M*g*h
After that Ek2 = ((I*w)/2) + ((M*v^2)/2)
Then Ep2 = 0
Now we Replacing values is:
That is 0 + M*g*h = ((I*w)/2) + ((M*v^2)/2) + 0
where:
M is = mass of the object
g is = gravitational acceleration
I is = moment of the inertia
w is = angular velocity = v/R
h is = height
M*g*h is = ((1/2) * I * (v^2/R^2)) + ((M*v^2)/2)
M*9.8*2 is = (I*(5.9^2)/(2*R^2)) + ((5.9^2 * M)/2)
19.6 * M is = ((17.4*I)/R^2) + 17.4*M
Now We mention Clearing I, we have:
Therefore, I is = 0.126*R^2*M
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