Students will apply the concept of centripetal force caused by friction to calculate the maximum speed at which a car can safely make a turn.

The force of friction is the centripetal force that allows vehicles to turn.

In the last lesson, Playing "A-Round" with Circular Motion, students were introduced to the concept of circular motion and the two important vectors used: centripetal force and tangential velocity. Now it is time for them to practice a variety of problems involving circular motion and the different types of forces that can provide centripetal forces, such as friction, tension and the normal force.

CCSS Math Practice 1 is applied in this lesson, as students make sense of problems and persevere in solving them. Also relevant to this class period is NGSS Science Practice 5, as students use mathematics and computational thinking. Again, this is all in the context of the NGSS performance standard HS-PS2-1 as students apply Newton’s Second Law of motion to several different situations.

20 minutes

Class starts off with Centripetal Forces power point displayed. A sample problem is presented on the first slide involving the centripetal force required to keep the blades of a windmill rotating. Students are informed that they are to complete this problem in their notebooks. I wait for students to write down the variables then I show the next slide that has the needed equations. I give students five minutes to work through the problem, they are free to ask questions and work with a neighbor.

As students work through the problem and the calculations, I stress to them how huge these blades are. In many cases they are longer than a school bus. The reason for this is I want them to get an idea of the scale of these windmill blades, because after we review the solution to the "do now" activity, I show them a video of a windmill gone crazy! It is a Youtube video that shows a windmill blade disintegrating because the forces required to maintain the circular motion where not strong enough.

While the video plays, I go around the classroom and check to see if students completed last night's homework. Sometimes I collect homework and grade it for the purpose of assessment, but for this assignment I check to see evidence that students listed the variables and did the work. If they show good effort, they get full credit. Tomorrow's assignment will be collected and assessed for student understanding, but for now I am checking to make sure they are doing the work.

As a class we discuss the video as I ask questions about why the blade came apart. It is the perfect video to show in the context of circular motion and results in wide-eyed students who ask great questions about the situation.

After we are done discussing the video, we review the homework. I scan the solutions and place them in the power point, so that students can see the answers I provide. As we review the homework, students are expected to correct any mistakes they have on their sheets.

20 minutes

After the discussion about the force involved with making a windmill blade go in a circle, I expand the discussion and ask students to shout out as many different forces as they can think of that might cause circular motion. I get all of the answers they are familiar with such as: normal, tension, gravity. If no one mentions friction, I ask the question to the class about cars and what force is responsible for making a car turn. Some say the steering wheel, others the tires, but eventually someone says friction. If not, I can ask what happens if you turn the wheel when the car is on ice. With that, the students understand that friction is the force responsible for making a car turn.

I hand out the Circular Motion and Friction Question which has the students apply the concept of circular motion to a car departing a highway via a curved off-ramp. This is a real-life problem that civil engineers have to take into account when designing roads. Copied off of Google Maps, I include a picture of a familiar highway exit about a mile from the high school. Again, I find it beneficial to use real-life examples and expand students' thinking about the many applications of physics around them. The students have to identify the variables they need, measure the radius of the circle with the scale provided on the Google Maps picture. I point out that the scale is in feet, and that might lead to problems in the calculations if they don't pay attention to the units. Students must also determine the applicable formulas which are the formulas for centripetal force and the force of friction (both listed on the Formulas for Car Turning). I give hints to students if they get stuck with this.

Students then identify the applicable variables and formulas and work through this multi-step problem. They work with neighbors, but everyone is responsible for their own paper which I collect for a grade at the end of the class. If one sets the friction formula equal the centripetal force formula, the Circular Motion Answer Key is relatively easy to figure out.

With a few minutes remaining in the period, I end the class with a series of questions about exit ramps, students raise their hands to answer them. These questions are applications of the centripetal motion as it applies to exit ramps and are a good closure.

- What force allows a car to make the turn? (answer - friction)
- How does the curve change? (answer - radius grows smaller)
- Why is it ok that the radius gets small as the cars travel on the ramp? (answer - cars slow down so less force is needed to keep them on the curve)
- If you were to place a guard rail on the ramp, where would you put it? (answer - the outside edge of the curve)

I collect the sheets as students exit.