A point mass of mass m is moving on a frictionless surface towards a thin rod, as shown in the diagram below. The mass of the rod is 2m and its length is L. The initial velocity of the point mass is vo and it points perpendicularly to the bottom of the rod. The point mass collides with the system disc-rod at the lowest point of the rod (as shown in diagram). The collision is perfectly inelastic and the point mass sticks to that impact point. You can use: Iyod.coM =ML2 (rod of length L and mass M) 2m vo m a) Find the center of mass and rotational inertia (around its COM) of the system after collision (disc and rod), in terms of the given parameters (m and L). b) Find the final linear velocity of the system after collision, in terms of the initial velocity of the point mass, vo. c) Find the final angular velocity of the system after collision, in terms of vo and L. If you did not find the answers to a) and b) use: RCOM =L (measured from the bottom of the rod), Isyst. =ml? and v.coM =Vo (in the same direction as vo). COM
A point mass of mass m is moving on a frictionless surface towards a thin rod, as shown in the diagram below. The mass of the rod is 2m and its length is L. The initial velocity of the point mass is vo and it points perpendicularly to the bottom of the rod. The point mass collides with the system disc-rod at the lowest point of the rod (as shown in diagram). The collision is perfectly inelastic and the point mass sticks to that impact point. You can use: Iyod.coM =ML2 (rod of length L and mass M) 2m vo m a) Find the center of mass and rotational inertia (around its COM) of the system after collision (disc and rod), in terms of the given parameters (m and L). b) Find the final linear velocity of the system after collision, in terms of the initial velocity of the point mass, vo. c) Find the final angular velocity of the system after collision, in terms of vo and L. If you did not find the answers to a) and b) use: RCOM =L (measured from the bottom of the rod), Isyst. =ml? and v.coM =Vo (in the same direction as vo). COM
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A point mass of mass m is moving on a frictionless surface towards a thin rod, as
shown in the diagram below. The mass of the rod is 2m and its length is L. The
initial velocity of the point mass is vo and it points perpendicularly to the bottom
of the rod. The point mass collides with the system disc-rod at the lowest point of
the rod (as shown in diagram). The collision is perfectly inelastic and the point
mass sticks to that impact point.
You can use:
Irod.coM =ML? (rod of length L
%3D
and mass M)
2m
L
vo
a) Find the center of mass and rotational inertia (around its COM) of the system after
collision (disc and rod), in terms of the given parameters (m and L).
b) Find the final linear velocity of the system after collision, in terms of the initial
velocity of the point mass, vo.
c) Find the final angular velocity of the system after collision, in terms of vo and L. If
you did not find the answers to a) and b) use: RCOM =L (measured from the
bottom of the rod), Isyst. =mL? and v.cOM =vo (in the same direction as vo).
%3D
COM
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