11thanks Subhomoy.
1)The torque of the weight of any body about any vertical axis is 0. Is it always true?
2)A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?
3) When several forces acts on a particle we take the torque of the resultant force. Is this result valid for the force acting on different particles of a body in such a way that their lines of action intersect at a common point ?
4)In pure rolling angular velocity is independent of the distance r from the axis of rotation. Why ?
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5 Answers
49i dont think torque is zero for ANY vertical axis..
T=rXF
and for any vertical axis θ between r and F is 90°
Thus, T=rF
Now since the axis is vertical, it provides a reaction force which creates a torque in opposite sense as created by weight!
thus the torque due to weight is balanced and doesnot create any change in the state of the body! [1]
49supposing sphere has angular velocity ω...then its Centre's velocity is rω
so....
from figure,
for velocity becoming purely perpendicular,
rωsinθ=rω
giving θ=90°,
which gives perpendicular velocity 0
thus, no such point possible in ground frame of reference
HOWEVER, FROM FRAME OF REFERENCE OF CENTRE OF SPHERE, 2 SUCH POINTS, THOSE FORMED BY INTERSECTING POINTS OF SPHERE SURFACE AND HORIZONTAL DIAMETER, ARE POSSIBLE!!
49pure rolling or not
ANGULAR velocity is same for all points of a body at a point on time-axis! ;P
think n this u will get the reason urself!
49for 3)
it is ideal not to do that
just take individual forces and find out torque and then find resultant rather than finding resultant force and then torque...
at most what u can do is
consider all the forces acting at same perpendicular distance from the centre, and add up the components of force in the same direction and then find torque!