Question Video: Calculating the Rotational Kinetic Energy of a Football Physics • 9th Grade

A football is rotating with an angular velocity of 28 rad/s. The football has a moment of inertia of 1.9 kg.m² around its axis of rotation. What is the rotational kinetic energy of the football? Give your answer to 2 significant figures.

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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.

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