The story of a mercilessly thrown sphere...

Classical Mechanics Level 3

A spherical ball of mass M and radius R is thrown along a rough horizontal surface so that initially, it slides with a linear speed \(\displaystyle{\upsilon_0}\),but does not rotate. As it slides, it begins to spin and eventually rolls without slipping. The time taken to start rolling can be expressed as \[\dfrac{a}{b} \times \dfrac{\upsilon_0}{\mu_k g}\] Where \(\displaystyle{\mu_k}\) is the coefficient of kinetic friction between the surface and the ball .What is \(\displaystyle{a+b}\)?

Liked it? try some more

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.