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A billiard ball initially at rest is given a sharp impules by a cue. The cue is held horizontally at a distance h above the centre line as in figure. The ball leaves the cue with a speed v and eventually acquires a speed 9/7 v. Show that h=4R/5, where R is the radius of the ball. My attempt- The friction force acts in the direction of motion as angular velocity is greater than linear speed (backward slipping occurs). considering rotation about central axis, fR=I(alpha) where (alpha) is the angular acceleration. I can get 2 equations relating linear speed at time t and angular speed at time t. But I don't know how to relate impulse with speed of the ball. I also wanted to ask that if we consider rotation about the point of contact, there is no torque acting on the sphere. How do we proceed this way?

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A billiard ball initially at rest is given a sharp impules by a cue. The cue is held horizontally at a distance h above the centre line as in figure. The ball leaves the cue with a speed v and eventually acquires a speed 9/7 v. Show that h=4R/5, where R is the radius of the ball.


 


My attempt-


 


The friction force acts in the direction of motion as angular velocity is greater than linear speed (backward slipping occurs).

considering rotation about central axis,
fR=I(alpha) where (alpha) is the angular acceleration.
I can get 2 equations relating linear speed at time t and angular speed at time t.

But I don't know how to relate impulse with speed of the ball.
I also wanted to ask that if we consider rotation about the point of contact, there is no torque acting on the sphere. How do we proceed this way?


 


 


 

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

linear impulse is integral of force w.r.t. time. it is equal to change in linear momentum. Angular impulse =

r X linear impulse =change in angular momentum

these two conditions will lead to the required equations

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