Q NUMBER 5 NEED TO BE ANSRWED An object is formed by attaching a uniform, thin r

Question

Q NUMBER 5 NEED TO BE ANSRWED

An object is formed by attaching a uniform, thin rod with a mass of mr = 7.32 kg and length L = 5.72 m to a uniform sphere with mass ms = 36.6 kg and radius R = 1.43 m. Note ms = 5mr and L = 4R.

1) What is the moment of inertia of the object about an axis at the left end of the rod?

1980.85 kg-m2

2) If the object is fixed at the left end of the rod, what is the angular acceleration if a force F = 401 N is exerted perpendicular to the rod at the center of the rod?

0.5789 rad/s2

3)

What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)

162.16 kg-m2

4)If the object is fixed at the center of mass, what is the angular acceleration if a force F = 401 N is exerted parallel to the rod at the end of rod?

0 rad/s2

5)

Q What is the moment of inertia of the object about an axis at the right edge of the sphere?

kg-m2

Explanation / Answer

moment of inertia of the rod about an axis passing through its center of mass=(mr*L^2)/12

distance between the axis shown to the right of the sphere and the axis passing through the center of mass of the rod

=2*R+(L/2)

=2*R+(4*R/2)

=4*R

using parallel axis theorem,

moment of inertia of the rod about the axis shown in the image

=moment of inertia about axis through center of mass + mass*distance between two axes^2

=(mr*L^2/12)+mr*(4*R)^2

=(7.32*5.72^2/12)+7.32*(4*1.43)^2

=259.457 kg.m^2

moment of inertia of the sphere about an axis passing through its center of mass=0.4*ms*R^2

distance between two axes=R

so total moment of inertia of the sphere using parallel axis theorem

=0.4*ms*R^2+ms*R^2

=104.78 kg.m^2

so total moment of inertia of the system about the axis shown

=259.457+104.78

=364.2376 kg.m^2

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.