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I am trying to simulate this situation.

Suppose that I have a Ball (sphere) in Vacuum with no forces acting on it. Now If I apply a force at a point on the surface of the ball, the force can be broken into 2 components. One, perpendicular to the surface, going through the point on surface and Center (also the Center of Mass) of the ball. This will cause linear motion of the ball, which can be calculated using

$$ \ F = ma\, $$

The second component would be perpendicular to the first component and parallel to the surface at the point of application of force. This component will cause angular motion of the ball with Torque calculated using, $$ \tau = F \times r\, $$

Then using $$ \tau = I \times \alpha\ $$ I can calculate angular acceleration.

Am I thinking correctly? Am I missing something?

Thanks

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  • $\begingroup$ Have a look at Chasles’s theorem in the appendix of this document web.mit.edu/8.01t/www/materials/modules/chapter20.pdf $\endgroup$
    – Farcher
    May 16, 2018 at 6:30
  • $\begingroup$ I am not sure how that applies to my problem. What I am concerned about is finding force components that produce translation and rotation. Do I must deal with friction? $\endgroup$
    – irobot96
    May 17, 2018 at 5:09
  • $\begingroup$ My understanding is that without any Friction, there would be no rotation. $\endgroup$
    – irobot96
    May 17, 2018 at 5:18
  • $\begingroup$ With no other forces present if the line of action of the applied force does pass through the centre of mass of the body then the body will undergo translation and rotation. $\endgroup$
    – Farcher
    May 17, 2018 at 5:45
  • $\begingroup$ In the case of a sphere, the line of action of force passing through the center means that it is in radial direction. It won't produce any rotation in this case, just translation. Can you explain what you meant a little more? $\endgroup$
    – irobot96
    May 17, 2018 at 21:06

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