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In this lesson, we will learn how to calculate the moment of inertia of a system given the rotational motions of its components.
A uniform rod of mass 1.0 kg
and length 2.0 m is free to rotate about one of its ends, as shown in the accompanying diagram.
If the rod is released from rest at an angle of
above the horizontal,
what is the speed of the tip of the rod as it passes the horizontal position?
The major and minor radii of a thin elliptical disk of uniform density are
2.00 m and
1.00 m, respectively. The disk has a
mass of 1.00 kg. Determine the moment
of inertia about an axis that is perpendicular with the disk’s surface and intersects the
center of the disk.
How do shear stresses and normal stresses differ?
What is the dimension of mass moment of inertia?
A solid sphere of radius 10 cm is allowed to rotate
freely about an axis. The sphere is given a sharp blow so
that its centre of mass starts from the position shown in the
following figure with speed 15 cm/s.
What is the maximum angle that the diameter makes with the vertical?
Which of the following formulas correctly expresses the relationship between the mass moment of inertia
and the radius of gyration
for an object of mass
A rod and a sphere are combined to form a system. The rod’s length
is 0.50 m and its mass is 2.0 kg. The sphere’s radius
is 20.0 cm and its mass is 1.0 kg. The system can rotate either about the point
, at the opposite end of the rod to the sphere, or about the point
, where the rod and the sphere connect, as shown in the diagram.