Answer: 0.126
Step-by-step explanation:
To calculate the ratio of the rotational energy to the translational kinetic energy of a baseball, you need to first calculate the rotational energy and the translational kinetic energy of the ball.
The rotational energy of a uniform sphere is given by:
E_rot = (1/2) * I * ω^2
where I is the moment of inertia of the sphere and ω is the angular speed.
The moment of inertia of a uniform sphere of radius r is:
I = (2/5) * m * r^2
where m is the mass of the sphere.
The translational kinetic energy of a moving object is given by:
E_trans = (1/2) * m * v^2
where m is the mass of the object and v is its speed.
Substituting these equations into the expression for the ratio of rotational energy to translational kinetic energy, we get:
(E_rot / E_trans) = [(1/2) * (2/5) * m * r^2 * ω^2] / [(1/2) * m * v^2]
= (2/5) * r^2 * ω^2 / v^2
Plugging in the values for the baseball, we get:
(E_rot / E_trans) = (2/5) * (4.07 cm)^2 * (155 rad/s)^2 / (31.3 m/s)^2
= 0.126