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.
