Calculate Final Velocity of a Ball that Slides then Rolls Without Slipping

A ball is thrown at some initial velocity Vi along a rough surface. Initially the ball is only experiencing translational, or linear, motion. After some time the torque by friction causes the ball to experience rotational motion as well. Eventually the translational velocity of the ball and tangential velocity of the ball are equal and the ball rolls without slipping.

[youtubeessentials]

wow . awesome . as a computer enigeering student, this video helped me a lot . thank you

[murattoprak]

Excellent explanation, keep up the great work!

[ptyptypty]

great VIdeo !! so well done... Amazing how the RESULT is a constant for ALL solid Spheres and that Coefficient of Friction is NOT a factor... who knew? Thank you... I saved your video to my Facebook page for others to see... :)

[Suprdud]

This always confused me because, essentially, the ball is assumed to have no work being done due to friction. This can not be entirely correct because the velocities will have to decrease due to elastic deformation. This can be understood by using the elastic modulus. The resistance will be related to some constant times the normal force: Cr. The angular deceleration due to this is 5/2(Cr*g/R) where g is gravity and R is the radius of the wheel. The linear deceleration with be Cr*g.

[BBQsquirrel]

Great video and explanations, but I have the following corollary: If the sphere is initially set to be rolling without slipping already, what will be 1) the frictional force 2) the v-t relationship and 3) the w-t relationship?

[m.f.studios]

Amazing video with an amazing explanation! Keep up the good work!

[BenoitVerreault-wr]

Great! But can you do the same analysis for a duckpin bowling ball which is typically thrown with a backspin? I would be interested in seeing a graph of the tangential speed versus time and see how it evolves when the spin goes from back to forward.

[wongjason]

Is there still friction acting on the ball when the ball is rolling without slipping? If there is still friction, then the ball should continue to increase its rolling speed, right? Thank you for such a great video btw😊

[BenoitVerreault-wr]

I meant rubber-band duckpin bowling (10 pins) which seems to be mostly still played in Canada. Contrary to duck pin bowling where you throw your ball as fast as you can like a madman, rubber-band duckpin bowling relies on the release of the energy stored in the rubber-band after it has been hit by the ball. Therefore the ball is thrown with a backspin at a speed optimized such that the back spin will come to stop and begin a forward spin just as it arrives at the pin. Hence I would like to know how the tangential speed evolves over time! Thanks.

[munkhochirm]

can i find final angular velocity without radius

[toottoot]

Static friction and kinetic friction aren't necessarily the same