# Question Video: Calculating the Angular Speed of a Car Wheel Physics

The wheel of a car has a moment of inertia of 2.25 kg⋅m² about its axis of rotation. As the car is driven along a road, the wheel has an angular momentum of 70.7 kg⋅m²/s. With what angular speed is the wheel rotating?

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### Video Transcript

The wheel of a car has a moment of inertia of 2.25 kilograms meters squared about its axis of rotation. As the car is driven along a road, the wheel has an angular momentum of 70.7 kilograms meter squared per second. With what angular speed is the wheel rotating?

Let’s say that this is the wheel we’re considering and that as the car drives along, the wheel rotates about an axis through its center. This rotation happens at some angular speed, we’ll call it 𝜔, and it’s this value we want to solve for. We can do this by taking into account that we’re given the moment of inertia of the wheel as well as its angular momentum. We can recall that an object’s angular momentum 𝐿 is equal to its moment of inertia multiplied by its angular speed. And so we can equivalently write that angular speed is equal to angular momentum divided by moment of inertia.

In our scenario, the wheel’s angular momentum is 70.7 kilograms meter squared per second and its moment of inertia is 2.25 kilograms meters squared. Looking at the units in this expression, notice that kilograms and meters squared cancel out from top and bottom and that we’ll be left with one over seconds in our final answer. When we calculate our result, which to three significant figures has a numerical value of 31.4, we can recall that 𝜔, an angular speed, has units of radians per second. Now, the reason that radians didn’t appear in our fraction is that the radian is a dimensionless quantity. Nonetheless, it’s a unit that we know to include when we’re talking about angular motion, as in this case with angular speed. So the angular speed with which this car wheel is rotating is 31.4 radians per second.