The center of mass of a pitched baseball or radius 2.11 cm moves at 23.6 m/s. The ball spins about an axis through its center of mass with an angular speed of 139 rad/s. Calculate the ratio of the rotational energy to the translational kinetic energy. Treat the ball as a uniform sphere.

The ratio of the rotational energy to the translational kinetic energy is 0.00618.

Explanation:

The rotational kinetic energy of a solid sphere is given by

where m is its mass, r is its radius and ω is its angular speed.

The translational kinetic energy is given by

where v is its linear speed.

The ratio of the rotational energy to the translational kinetic energy is

From the question,

r = 2.11 cm = 0.0211 m

ω = 139 rad/s

v = 23.6 m/s

The ratio of the rotational energy to the translational kinetic energy is 0.00618

Explanation:

If m is the mass of the baseball and v its speed, then the translational kinetic energy is

Kt = 1/2 mv²

If I is its rotational inertia and ω is its angular speed, then the rotational kinetic energy is

Kr = 1/2 Iω²

But the rotational inertia of a uniform sphere is I = 2mr²/5

Therefore, the ratio of the rotational energy to the translational kinetic energy is 0.00618.

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.