3 particle each if mass m and charge q are attached to the vertices of a triangular frame made up of 3 light rigid rods of equal length l. The frame is rotated with a constant angular field omega about an axis perpendicular to the plane of triangle and passing through its centre . the ratio of magnetic moment if the system and the angular momentum about the axis of rotation is?
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11th
Physics
Systems of Particles and Rotational Motion
Dynamics of Rotational Motion
Three particles A,B,C each ...
PHYSICS
Three particles A,B,C each of mass m are connected to each other by three massless rigid rods to form a rigid, equilateral triangular body of side l. This body is placed on a horizontal frictionless table (x-y plane) and is hinged at point A so that it can move without friction about the vertical axis through A. The body is set into rotational motion on the table about this axis with a constant angular velocity ω (a) Find the magnitude of the horizontal force exerted by the hinge on the body (b) At time T, when side BC is parallel to x-axis, force F is applied on B along BC (as in the figure). Obtain the x-component and the y-component of the force exerted by the hinge on the body, immediately after time T.
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December 27, 2019
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Abira Winy
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ANSWER
The centre of mass of the system is at the centroid of a triangular assembly. The CM moves along a circular path with constant angular velocity. Therefore, there must be a horizontal centripetal force directed towards the axis at the hinge
From figure we find
AD=lsin60
o
=
2
l
3
AO=
3
2
AD=
3
l
2
=r
the centripetal acceleration a
c
=ω
2
r=ω
2
(
3
l
)
Tangential acceleration a
t
=αr=α(
3
l
)
(b) Let F
x
and F
y
be the forces applied by the hinges along x-axis and y-axis respectively. The system is in non-centroidal rotation. The three equations of motion are
∑F
x
=F
x
+F=(3m)a
t
=3m(
3
α
l
)...(i)
∑F
x
=F
y
+3m(
3
l
)ω
2
....(ii)
∑τ=F×(
2
3
l)=2ml
2
α....(iii)
From Eq (iii) α=
4ml
3
F
From Eq (i), F
x
+F=3m(
3
α
l
)×
4ml
3
F
=
4
3F
⇒F
x
=
4
F
from Eq. (ii) F
y
=
3
mlω
2
Explanation:
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