A bowling ball has a mass of 7.0 kg,a moment of inertia of 2.8 × 10−² kg·m²,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 2.5 m/s,what is its total kinetic energy? A) 30.6 J B) 8.8 J C) 21.9 J D) 25.0 J

Question

Quizplus · Accepted Answer

The total kinetic energy is the sum of translational and rotational kinetic energy. Translational KE = 0.5 * m * v^2 = 0.5 * 7.0 kg * (2.5 m/s)^2 = 21.875 J. Rotational KE = 0.5 * I * ω^2, where ω = v/r = 2.5 m/s / 0.10 m = 25 rad/s. Rotational KE = 0.5 * 2.8 × 10^-2 kg·m^2 * (25 rad/s)^2 = 8.75 J. Total KE = 21.875 J + 8.75 J = 30.625 J, approximately 30.6 J.

A Bowling Ball Has a Mass of 7