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It would be great if some of these problem specified now and then, relative to which frame of reference they use the words: displacement, velocity, trajectory, rotational speed, power of force, kinetic energy... @srujit : do you have an idea what the answer might be, (with respect to the ground)?
i am not getting the idea whether is there an angular rotation about the centre of the ball in addition to the (string+block) moving altogether at an angular velocity around the pivoted point ?
The question is: is the ball rotating wrt to the room you are in? To be sure, imagine a coloured line painted on the ball and a fixed line in your room (a vertical on your wall for instance). At t=0, both lines are parallel. Only if those lines stay parallel throughout the motion will it mean that the rotational speed of the ball is 0 wrt your room.
yeah i guess its asked with respect to room ! it would appear simple if described like this-the earth moves around the sun..revolution which the ball does around the pivoted point..as also the earth rotates around its own axis..so will here the ball rotate like that around its own axis?
Its completely similar to the Earth-Moon system, where only one side of the Moon can be seen from Earth.
yea so it rotates along its own axis of rotation( which is collinear to the string attached) ?
Almost: "it rotates along its own axis of rotation( which is collinear to THAT OF the string attached) "
but why does it need to rotate?
It does not "need" to rotate, it just does! If it were not rotating, the string would wind up around the ball.
ok got it !
Remember rotation means change in orientation relative to a reference body. I you can define an angle \(\theta\) from the room's vertical to a line on the ball, then its rotational speed is \(\omega = \dot \theta\) You will find that this angle is the same as between the vertical and the string itself. Hence: angular velocity of centre of ball = rotational speed of ball about its axis
yea right there!