The thin solid shaft of length L and radius r is fixed at one end. A rigid rod is attached to this shaft at the other end. The rigid rod is subjected to a set of equal opposite forces P at its ends perpendicular to the axis of the shaft as shown. The rigidity modulus of the material of the shaft is given by G. Determine the maximum tensile stress at point 'A' on the surface of the shaft
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11th
Physics
Systems of Particles and Rotational Motion
Dynamics of Rotational Motion
A uniform thin rod of lengt...
PHYSICS
A uniform thin rod of length L is hinged about one of its end and is free to rotate about the hinge without friction. Neglect the effect of gravity. A force F is applied at a distance x from the hinge on the rod such that force is always perpendicular to the rod. Find the normal reaction at the hinge as function of 'x' , at the initial instant when the angular velocity of rod is zero.
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December 27, 2019
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Sameera Suman
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ANSWER
At horizontal position the reaction 'N'.
Let the mass of rod is m.
The moment of inertia of rod about the axis passig through the end and perpendicular to its plane is
I=
3
1
ml
2
For rotation of rod,
Moment of force = Applied torque
⟹x×F=Iα
⟹α=
3
1
ml
2
xF
=
ml
2
3xF
Here α is angular acceleration about hinge .
The position of centre of mass is aat the middle.
So the linear acceleration of centre of mass,a=α
2
l
a=
2ml
3xF
So, the net force in vertical on centre of mass is
=ma
=
2l
3xF
This should be equal to N.
So, N=
2l
3xF