A hollow sphere is moving with linear velocity and angular velocity as shown in figure. The time after which pure rolling starts is:

Question

G1 Physics · Accepted Answer

For a hollow sphere I=2MR²/3. With the shown initial spin, kinetic friction changes v and ω until v=ωR. Solving gives t=4v/(5µg). Hence C. Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives 4v/(5µg)..