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.

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