RIGID BODY KINEMATICS -- Tricky question !!?
At the instant shown, OB has a counter clockwise angular velocity of 4 rad/s The distance x is 1.2m Find Vc, Vb Optional : find Va Image : http://img221.imageshack.us/img221/2609/… If the link is truncated, add imag0050w.jpg after 2609/... Anyone got an idea how to solve this ?? I know that Vb will have a force perpendicular to the body OB since the angular velocity is pointing at that direction ...and I know that Vb/o = w*L ... But Vo doesnt exist !! Only the angular velocity around O ... Can someone PLEASE explain in details what is going on here ? Thanks !!
What is Coriolis acceleration?
Coriolis force occurs when you move away or towards the center of rotation. That is because in a rotating frame of reference, like a rotating disk of five meter across in a playground, when you are half way between the center and the rim, your rotational speed is half that of the speed on the rim, and in the center it is zero of course. When you take two steps to the rim you do not yet have the required rotational speed and you therefore seem to have accelerated sideways against the direction of rotation. When you take more time moving to the rim the sideways acceleration seems smaller, because it takes more time for the rotational speed deficit to build up. That is why the size of the coriolis force scales linearly with the radial component of your speed relative to the center of rotation and its direction is perpendicular to the direction to the center of rotation.
If the lift goes up with acceleration "a" then the relative acceleration of a projected body with regards to lift is (g+a). How?
According to Newton's 3rd law of motion, for every action, there is equal and apposite reaction.When one stand on rigid surface, his weight (m × g) act in downward direction therefore surface exert equal and opposite reaction. This reaction is called normal reaction. Normal means perpendicular to surface.One can't stand on surface of water because water can't provide equal and opposite reaction. One can't run faster through sand because sand can't provide equal and opposite reaction to weight.When a person stands in stationary lift, his weight acts in vertically downward direction. When lift ascend in upward direction with acceleration a, reaction force f = (m× a) act in opposite direction i.e. vertically downward direction. This adds in his weight . Therefore his apparent weight becomes (mg + ma)(mg)’ = mg + maSolving this, g' = g + a , where g' is apparent acceleration. (mass remain constant)Similarly if lift descend in downward direction with acceleration a, reaction force acts in vertically upward direction, apparent acceleration is g - aWhen lift move with uniform speed, there is no acceleration, hence there is no change in weight. We experience jerk (change in acceleration per unit time) when lift ascend or descend with acceleration.Hope this will clear.
How all the particles of rigid body have same angular velocity?
consider a rigid rod, rotating about an axis attached to one end of it.if all particles of the rod don’t have same angular velocity, then rod has to bend, which is not possible as it rigid.now consider a circular disc rotating about an axis passing through centre and perpendicular to the plane of disc. all particles should have same angular velocity, otherwise the disc will distort.this true for irregularly shaped disc also.a 3D object can be thought of as made of many discs whose plane is perpendicular to axis of rotation. hence by same argument all particles should have same angular velocity.any particle traces out a circular path, with centre on axis of rotation.
Why the angular velocity is same for all the particles of a rigid body and what is it in non rigid body?
The angular velocity of every particle in a rigid body remains at its position. Thence, every particle sweeps equal angle in equal interval of time. And as far as non-rigid body is concerned, I believe that it's case in angular velocity is same as in a rigid body.
Is a reflection a rigid motion?
Yes. Rigid transformations maintain the original size. Translations, Rotations and reflections are all rigid transformations.Dilation is not a rigid transformation as it can change the original size.
Why does a rigid body rotate about its center of mass when external forces stop?
The center of mass of any object will continue to move with a constant velocity if the external forces acting on a body add up to 0. In other words, the center of mass can not accelerate in absence of a net external force.Rotation of a particle or point involves centrifugal/centripetal accelerations depending on your frame of reference.If a body was rotating, it will continue to do so to conserve angular momentumBut the Center of mass can not be accelerating, So the body will rotate around the center of mass.