The uniform solid block in Fig 10-38 has mass 0.172kg and edge lengths a = 3.5cm, b = 8.4cm, and c = 1.4cm. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces.
The rotational inertia about an axis through one corner and perpendicular to the large faces is, .
Masses and coordinates of four particles are
By using the concept of moment of inertia we can calculate the moment of inertia about its axis. For the slab, if the axis is not passing through the center, then we can use the parallel axis theorem to calculate the moment of inertia.
For solving parallel axis theorem, wecalculate the perpendicular distance from the axis passing through its center and corner.
According to the parallel axis theorem,
Substitute all the value in the above equation.
Therefore, rotational inertia about an axis through one corner and perpendicular to the large faces is, .
A rigid body is made of three identical thin rods, each with length, fastened together in the form of a letter H (Fig.). The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body is allowed to fall from rest from a position in which the plane of the H is horizontal. What is the angular speed of the body when the plane of the H is vertical?
At , a flywheel has an angular velocity of , a constant angular acceleration of , and a reference line at .
(a) Through what maximum angle will the reference line turn in the positive direction? What are the
(b) first and
(c) second times the reference line will be ?
At what (d) negative time and
(e) positive times will the reference line be at ?
(f) Graph versus , and indicate your answers.
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