Answer:
(a) I=0.01 kg.m²
(b) I=0.03 kg.m²
Explanation:
Given data
Mass of disk M=2.0 kg
Diameter of disk d=20 cm=0.20 m
To Find
(a) Moment of inertia through the center of disk
(b) Moment of inertia through the edge of disk
Solution
For (a) Moment of inertia through the center of disk
Using the equation of moment of Inertia
[tex]I=\frac{1}{2}MR^{2}\\ I=\frac{1}{2}(2.0kg)(0.20m/2)^{2}\\ I=0.01 kg m^{2}[/tex]
For (b) Moment of inertia through the edge of disk
We can apply parallel axis theorem for calculating moment of inertia
[tex]I=(1/2)MR^{2}+MD\\ Here\\D=R\\I=(1/2)(2.0kg)(0.20m/2)^{2}+(2.0kg)(0.20m/2)^{2}\\ I=0.03kgm^{2}[/tex]
(a) I=0.01 kg.m²
(b) I=0.48 kg.m²
Given:
Mass of disk ,M=2.0 kg
Diameter of disk, d=20 cm=0.20 m
To Find:
(a) Moment of inertia through the center of disk=?
(b) Moment of inertia through the edge of disk=?
Using the equation of moment of Inertia
[tex]I=\frac{1}{2} MR^2\\\\ I=\frac{1}{2}(2)(0.20)\\\\ I=0.01kgm^2[/tex]
We can apply parallel axis theorem for calculating moment of inertia
[tex]I=\frac{1}{2} MR^2+MD\\\\ I= \frac{1}{2}(2)(0.20)^2+(2)(0.20)\\\\ I=0.48kgm^2[/tex]
Note: R=D in this case
Thus,
(a) I (through the center) =0.01 kg.m²
(b) I (through the edge of the disk) =0.48 kg.m²
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