A uniform disc of mass `m` and radius `R` is projected horizontally with velocity `v_(0)` on a rough horizontal floor so that it starts off with a purely sliding motion at `t=0`. After `t_(0)` seconds, it acquires pure rolling motion as shown in the figure.
(a) Calculate the velocity of the center of mass of the disc at `t_(0)`.
Assuming that the coefficent of friction to be `mu`, calculate `t_(0)`.

A uniform disc of mass m and radius R is projected horizontally with velocity v_(0) on a rough horizontal floor so that it starts with a purely sliding motion at t= 0. After t_(0) seconds it acquires a purely rolling motion. (a) Calculate the velocity of the centre of mass of the disc at t_(0) (b) Assuming the coefficient of friction to be mu , calculate to. Also calculate the work done by the frictional force as a function of time and the total work done by it over a time t muchlonger than t_(0) .

A uniform ring of mass 'm' and radius 'R' is projected horizontally with velcoty v_(0) on a rough horizontal floor, so that it starts off with a purely sliding motion and it acquires a pure rolling motion after moving a distance d. If the coefficient of friction between the ground and ring is mu , then work done by the friction in the process is

A uniform ring of mass 'm' and radius 'R' is projected horizontally with velcoty v_(0) on a rough horizontal floor, so that it starts off with a purely sliding motion and it acquires a pure rolling motion after moving a distance d. If the coefficient of friction between the ground and ring is mu , then work done by the friction in the process is

A disc of mass M and radius R is rolling purely with centre's velcity v_(0) on a flat horizontal floor when it hits a step in the floor of height R//4 The corner of the step is sufficiently rough to prevent any slippoing of the disc against itself. What is the velocity of the centre of the disc just after impact?

A disc of mass M and radius R is rolling purely with centre's velcity v_(0) on a flat horizontal floor when it hits a step in the floor of height R//4 The corner of the step is sufficiently rough to prevent any slippoing of the disc against itself. What is the velocity of the centre of the disc just after impact?

A cylinder is rotating with angular velocity omega_(0) and is gently put on a rough horizontal floor. Assume mass of the cylinder is m and radius R. Calculate the velocity of cylinder when it starts pure rolling on the surface.

A uniform disc of mass m and radius R is thrown on horizontal lawn in such a way that it initially slides with speed V_0 without rolling. The distance travelled by the disc till it starts pure rolling is (Coefficient friction between the contact is 0.5)