Video Transcript
A tennis ball has a rotational
kinetic energy of 248 joules. Its moment of inertia around its
axis of rotation is 0.22 kilogram meter squared. What is the angular velocity of the
tennis ball? Give your answer to two significant
figures.
In our problem, we are given
rotational kinetic energy, moment of inertia, and we are asked to solve for the
angular velocity. This means that we need an equation
that relates these three variables together. We know that 𝑘, the rotational
kinetic energy, is equal to one-half 𝐼, the moment of inertia of an object, times
𝜔 squared, where 𝜔 is the angular velocity of the object.
Our problem asked us to solve for
the angular velocity of our tennis ball. Therefore, we must rearrange our
formula to solve for our unknown variable. To isolate 𝜔 squared, we must
multiply both sides of the equation by two and one over 𝐼. This will cancel out the one-half
on the right-hand side of the equation as well as the 𝐼 on the right-hand side of
the equation, leaving us with two times the rotational kinetic energy divided by the
moment of inertia is equal to the angular velocity squared. To turn 𝜔 squared into just 𝜔, we
must square root both sides of the equation. This will cancel out the square on
the right-hand side.
Now we have the square root of two
𝑘 over 𝐼 equals 𝜔, and we are ready to plug in our values. We replace 𝑘 with 248 joules and
𝐼 with 0.22 kilogram meter squared. When we calculate our angular
velocity, we get 47.48 radians per second. This, however, is not our final
answer as we are asked to give our answer to two significant figures. When we round 47.48 radians per
second to two significant figures, we get 47 radians per second. The angular velocity of the tennis
ball is 47 radians per second.
