A uniform rod of length and mass
is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Figure. There is no friction at the pivot. An inelastic ball of mass
is fixed with the rod at a distance
from
A horizontal impulse
is given to the rod at a distance
from
in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse
acts for a small time interval
t
Now answer the following question
Find the resulting instantaneous angular velocity of the rod after the impulse |
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a) |
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b) |
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c) |
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d) |
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A uniform rod of length and mass
is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Figure. There is no friction at the pivot. An inelastic ball of mass
is fixed with the rod at a distance
from
A horizontal impulse
is given to the rod at a distance
from
in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse
acts for a small time interval
t
Now answer the following question
Find the resulting instantaneous angular velocity of the rod after the impulse |
|||||||
a) |
|
b) |
|
c) |
|
d) |
|
(b)
Let the system starts with angular velocity . Angular velocity of the ball will also be
as it remains struck to the rod
Velocity of the ball
For the rod, angular impulse= change in angular momentum:
(i)
For the ball, impulse= change in linear momentum
(ii)
From Eqs. (i) and (ii),
and
Let impulse on the pivot be
For the rod and ball system, total impulse change in linear momentum
Solve to get: