While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75 kg m^2 and its rotational kinetic energy is 175 J. What is the angular velocity of the leg, in rad/s?
The formula for rotational kinetic energy is given by:
\(KE = \frac{1}{2} I \omega^2\)
where:
KE = rotational kinetic energy (175 J)
I = moment of inertia (3.75 kg m^2)
ω = angular velocity
Substitute the given values into the equation:
\(175 = \frac{1}{2} \times 3.75 \times \omega^2\)
Solve for ω:
\(175 = 1.875 \omega^2\)
Divide by 1.875:
\(\omega^2 = \frac{175}{1.875} = 93.33\)
Take the square root of both sides to find ω:
\(\omega = \sqrt{93.33} = 9.66 \, rad/s\)
Therefore, the angular velocity of the leg is 9.66 rad/s.