Motion in two dimension problemsssssss?

Question

a circular disc rotates in vertical plane about a fixed horizontal axis which passes through a point X on the circumference of the disc.when the center of the disc moves with speed V,the speed of the opposite end of the diameter through X will be??

i dont understand this question so help me

also when a stone is thrown at a certain angle with the vertical.before the stone attains its maximum height,a tiny piece separates from the stone.this piece will:

1.fall side by side with its parent stone

2.fall vertically down

also what will be the motion of that piece if the stone had attained maximum height when that piece separated?

thankssss

Answer 1

I can't make much sense out of the first question.

"when the center of the disc moves with speed V" -- the center of a rotating disk doesn't move with any linear speed. It rotates only.

also "fixed horizontal axis which passes through a point X on the circumference of the disc" how can the axis pass through the circumference?

Unless the disc is not rotating about it's center, but rather wobbling about a point on it's circumference. If that's the case, and the "center" moves with V, then the point opposite the axis will move with 2V (it's twice as far from the rotation point)

number 2, neither answer is correct. The pieces are still on their upwards trajectory, so they will both continue to rise, reach the peak of their trajectory, then fall together. Wind resistance will probably cause the pieces to separate at some point.

number 3, the motion will be the same as the larger piece. It will fall down under under the influence of gravity.

.

Answer 2

Question: -a circular disc rotates in vertical plane about a fixed horizontal axis which passes through a point X on the circumference of the disc.when the center of the disc moves with speed V,the speed of the opposite end of the diameter through X will be??

i dont understand this question so help me

Answer: In this question, the disc is not rotating around its centre but around some other point. That point is called as X.

Let x = distance of point X from centre of the disc

r = radius of the disc.

It is given that V = speed of point X.

Let Vd = speed of point on the opposite end of diameter through X.

Vd = ?

Angular speed of X = V/x

Angular speed of point on the opposite end of diameter = Vd/r

Angular speed of any point on the disc is same.

Therefore, Vd/r = V/x

Or, Vd = V*(r/x)

Ans: V multiplied by radius of disc divided by distance of point X from centre of disc.

Question: also when a stone is thrown at a certain angle with the vertical.before the stone attains its maximum height,a tiny piece separates from the stone.this piece will:

1.fall side by side with its parent stone

2.fall vertically down

Answer: It will move side by side with the parent stone because initial velocity of the piece is the same as the velocity of the parent stone when the stone breaks. We shoudl say "move side by side" and not "fall side by side".

Question: also what will be the motion of that piece if the stone had attained maximum height when that piece separated?

Fall side by side because of same reason related to initial velocity. In this case, they will fall because maximum height has been reached and after that the stone falls.