Rotational Energy

---

So far, we have covered kinetic energy, and frictional energy. Since we have covered one more kind of dynamic to the cue ball, we must consider the rotational energy.
K_t = (1/2)mv²
F_d = f_kDx
K_r = (1/2)Iw²

When the ball is slipping it means that the ball is translating without any rotation. Then when it begins not to slip, there is rotation however don't forget that there is also its corresponding tangential velocity. The center of the ball, is not rotating but rather simply translating in all cases. And in this special non-slip case, the acceleration and the velocity of the center of mass is given by:
v_cm = wR
a_cm = aR
Where R is the radius of the rotating object.

A cue ball is moving and slips for 5 meters then begins to roll without slipping and there is zero net external force, how do we describe this using conservation of energy?

E_i = (1/2)mv_cm² + f_k(5)
E_f = (1/2)mv_cm² + (1/2)Iw²
The intial state of energy is given by the kinetic energy of translation and the mechanical dissipation through friction. The final state of energy is given by the kinetic evergy of the object's tangential velocity and its energy of rotation.

Sample Problem
A cue is slipping at 10rev/s for 10m and hits an object ball which was initially at rest. The object ball begins to roll without slipping and the cue comes to rest at moment of impact. What is the angular velocity of the object ball? (m_k = 0.25, R = 5cm and equal masses for both balls)

Your Answer:

Solution