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A spherical ball is placed on a frictionless surface initially at rest. The ball then is given a sharp impulse J at a height h from the horizontal centre line. Find the angular velocity "w" (omega) and velocity of centre of mass Vcm if the mass of the ball is M and radius is R. Also find the value of h for which it will perform pure rolling on the surface.

A spherical ball is placed on a frictionless surface initially at rest. The ball then is given a sharp impulse J at a height h from the horizontal centre line. Find the angular velocity "w" (omega) and velocity of centre of mass Vcm if the mass of the ball is M and radius is R. Also find the value of h for which it will perform pure rolling on the surface.

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4 Answers

Anonym123
12 Points
6 years ago
Let the force of the impact be `F` thus (J= F×t) now this force creates a torque that is equals to `I × alpha(since there is no sign for alpha)` now ` alpha` equals (a÷R) and `I` for a solid sphere equals {( 2÷5)M(R)^2} which basically gives F={(2÷5)MaR} now if this force is multiplied by `t` we get J={(2÷5)MatR} making `a×t` the subject get {(5J)÷(2MR)} note that is basically the velocity of the center since the ball starts from rest and W= v÷R={(5J)÷2M(R)^2} and by consecutive now by using Mgh=(1÷2)I(W)^2 we get h=[{5 (J)^2}÷{4(M^2) g(R)^2}]
Anonym123
12 Points
6 years ago
Sorry about the last part in the sum to find h we have to write Mgh =.5IW^2+.5Mv^2 which will give us h={45J^2÷(16MR^2)}
Gitanjali Rout
184 Points
5 years ago
et the force of the impact be `F` thus (J= F×t) now this force creates a torque that is equals to `I × alpha(since there is no sign for alpha)` now ` alpha` equals (a÷R) and `I` for a solid sphere equals {( 2÷5)M(R)^2} which basically gives F={(2÷5)MaR} now if this force is multiplied by `t` we get J={(2÷5)MatR} making `a×t` the subject get {(5J)÷(2MR)} note that is basically the velocity of the center since the ball starts from rest and W= v÷R={(5J)÷2M(R)^2} and by consecutive now by using Mgh=(1÷2)I(W)^2 we get h=[{5 (J)^2}÷{4(M^2) g(R)^2}].
Gitanjali Rout
184 Points
5 years ago
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