Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Consider a flat rectangular plate of known mass, width and breadth with a negligible thickness that lies in the horizontal xy-plane. The plate is suspended from a thin piece of piano wire that is in the vertical orientation coincident to the z-axis and where the piano wire is attached to the center of the plate. When the plate is subjected to a torque whose vector is coincident to the z-axis, the plate rotates in the horizontal plane such that the rotation of the plate is modelled as θ=Csin(ωnt+ϕ).
The parameter information is:
mass of plate M = 1.2 kilogram
width of plate W = 0.040 meter
breadth of plate B = 0.075 meter
shear modulus of piano wire G = 79.3 gigaPascals
diameter of piano wire D = 0.003 meter
length of piano wire L = 0.120 meter
amplitude of rotation C = 0.087267520415 radian
phase lag of rotation ϕ = 1.565872597159 radian
Using the supplied information and any appropriate assumptions and / or approximations to determine the following;
1) the mass moment of inertia I
2)…
(Please explain)In a collision of disks, where the system is not isolated because of the existence of friction. How is it possible that conservation of angular momentum is still valid to a relatively good accuracy?
Prove that the time rate of change of angular momentum is equal to the torque acting on the system without using the differentiation concept.
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- A conical pendulum consists of a bob of mass m in motion in a circular path in a horizontal plane as shown in Figure. During the motion, the supporting wire of length "l" maintains the constant angle " theta " with the vertical. Show that the magnitude of the angular momentum of the bob about the center of the circle is:arrow_forwardShow that the moment of inertia of a rectangular plate of mass m and sidesa and b about the diagonal isarrow_forwardThree identical masses m are located at the three corners of an equilateral triangle with sides a in the xy-plane, with its base along the x-axis. Find their center of mass rCM and moments of inertia I with respect to (a) an axis through the center of mass parallel to the x-axis and (b) an axis through the center of mass parallel to the y-axis.arrow_forward
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