Video Transcript
A football is rotating with an
angular velocity of 28 radians per second. The football has a moment of
inertia of 1.9 kilogram meter squared around its axis of rotation. What is the rotational kinetic
energy of the football? Give your answer to two significant
figures.
In the problem, we are given
angular velocity, moment of inertia, and asked to solve for the rotational kinetic
energy. To begin to solve the problem, we
need to start with an equation that has these three variables in it. We can use the equation 𝑘 equals
one-half 𝐼𝜔 squared, where 𝑘 is the rotational kinetic energy, 𝐼 is the moment
of inertia, and 𝜔 is the angular velocity. In our problem, we are asked to
solve for the rotational kinetic energy of the football, which means we do not need
to rearrange our formula to solve for our unknown variable.
Plugging in the values given from
the problem, we have 1.9 kilogram meter squared for 𝐼 and 28 radians per second for
𝜔. Before we multiply out our values,
we must make sure that we square our angular velocity. When we multiply out our values, we
get a kinetic energy of 744.8 joules. This is not our final answer as the
problem asked us to give our answer to two significant figures. When we round 744.8 joules to two
significant figures, we get 740 joules. The rotational kinetic energy of
the football is 740 joules.
