Question

Calculate the translational speed of a cylinder when it reaches the foot of an incline 7.35 m high. assume it starts from rest and rolls without slipping.

Answer 1

The total kinetic energy will be equivalent to the potential energy;
The total kinetic energy is given by the sum of transitional kinetic energy and the rotational kinetic energy.
Rotational kinetic energy
I= 1/2mR², but rotational energy =1/2 I w² 
Thus  rotational energy is equal to 1/4 mR²w², which is equivalent to 
 = 1/4 mv² since v= wR
Thus;
Total kinetic energy = 1/2 mv² + 1/4 mv²
hence;
 Mgh = 3/4 mv²
  gh = 3/4 v² ( assuming g = 9.81 m/s²)
   72.1035 = 3/4 v²
v = 9.805
    = 9.805 m/s