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valentin68 | College Teacher | (Level 3) Associate Educator

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Mass is an intrinsic property of matter regardless its other physical properties like for example its form. Thus deforming an object does not change its mass.

Moment of inertia of an object is defined as

`I =int R^2*dm = sum_(i=1)^(+oo) R_i^2*m_i`

where the integral is taken over all the volume on the object. If you deform the object, you change its volume, hence you change the integration limits and the value of the inertia moment (or equivalent you change the values of individual `R_i` in the sumation).

Mass center is defined as

`R_(cm) = 1/M *int R*dm 1/M sum_(i=1)^(+oo) R_i*m_i`

where the integral is taken again over all the volume of the object. The same considerations as for the moment of inertia aplly also here.


The acceleration of the block comes from

`h =(a*t^2)/2 rArr a =2*h/t^2 =2*1.5/4 =0.75 m/s^2`

The angular acceleration `epsilon` of the wheel comes from

`a =epsilon*R rArr epsilon =a/R =0.75/0.4 =1.875 (rad)/s^2`

The torque on the wheel is

`T =F*R =20*0.4 =8 N*m`

and the relation between torque and angular acceleration is

`T =I*epsilon`    (analog `F =m*a` )

It means

`I =T/epsilon = 8/1.875 =4.267 kg*m^2 `

The moment of inertia of the wheel is `I =4.267 kg*m^2`