The document shows the steps to calculate the total kinetic energy of a solid sphere rolling without friction that has a mass of 3.25 kg, diameter of 20 cm, and linear speed of 1.41 m/s. It first calculates the translational kinetic energy as 3.23 J, then the rotational kinetic energy as 1.29 J using the moment of inertia and angular speed formulas. The total kinetic energy is calculated to be the sum of the rotational and translational energies, which equals 4.52 J.

1. Please help answer and show steps and work, thank you!!
5) A solid 3.25-kg sphere with a 20.0-cm diameter rolls without friction. Its linear speed is
1.41m/s. Calculate its total kinetic energy (linear + rotational).
Solution
translational kinetic energy KEtrans = (1/2)*m*v^2
KEtrans = (1/2)*3.25*1.41^2 = 3.23 J
rotational kinetic energy KErot = (1/2)*I*w^2
I = moment of inertia = (2/5)*m*R^2
w = angular speed = v/R
rotational kinetic energy KErot = (1/2)*(2/5)*M*R^2*(v/R)^2
KErot = (1/5)*m*v^2 = (1/5)*3.25*1.41^2 = 1.29 J
total kinetic energy KEtot = KErot + KEtran
KEtot = 1.29 + 3.23 = 4.52 J