Question Video: Calculating the Tangential Speed of a Car on a Circular Road Physics

A car is being driven around a circular road. The car has a mass of 2,300 kg, and the road has a radius of 40 m. If the car has an angular momentum of 7.36 × 10⁵ kg⋅m²/s, what is its tangential speed?

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Video Transcript

A car is being driven around a circular road. The car has a mass of 2300 kilograms, and the road has a radius of 40 meters. If the car has an angular momentum of 7.36 times 10 to the fifth kilogram meters squared per second, what is its tangential speed?

This question centers around a car on a circular road. We’re given several pieces of information: the radius of the road, the mass of the car, as well as the car’s angular momentum. We’re also asked to find the car’s tangential speed. Let’s draw a diagram to help organize all of this information. Here’s our diagram labeled with values from the question. We have the circular road with its radius of 40 meters. We have the car with its mass of 2300 kilograms. And we’ve also marked the angular momentum of the car 7.36 times 10 to the fifth kilograms meters squared per second. Finally, since the question doesn’t specify, we’ve chosen to draw the direction of motion of the car as clockwise. And we’ve marked the unknown tangential speed, which is what the question asks us to find.

Since we’re given the angular momentum of the object and the presumed reference point is the center of the circle since the question doesn’t specify otherwise, let’s write down the formula for the angular momentum of an object moving in a circle. We have that the size of the angular momentum about the center of the circle is equal to the radius of the circle times the mass of the object times its tangential speed. To solve this expression for tangential speed, we need to divide both sides by radius times mass. When we do this, on the left-hand side, we just get 𝐿 divided by 𝑟 times 𝑚. On the right-hand side, 𝑟𝑚 divided by 𝑟𝑚 is just one, and we’re left with the tangential speed.

Before we plug in values to this expression, note that 7.36 times 10 to the fifth is just 736000. So, taking the values that we’re given, we have that the tangential speed is equal to 736000 kilograms meters squared per second divided by 40 meters times 2300 kilograms. Simplifying units, the factor of kilograms in the numerator cancels the kilograms in the denominator. And the factor of meters in the denominator cancels one factor of meters in the numerator. We’re left with final units of meters per second, which tells us we’re on the right track because meters per second is a unit of speed. Okay, all that’s left to do is plug 736000 divided by 40 times 2300 into a calculator. This comes out to exactly eight. And carrying over the units, we have that the tangential or linear speed of the car is eight meters per second.

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