Background: Taking a moment to consider the validity of this equation can help to clarify what it means. Imagine a yo-yo. Instead of using it normally, let it fall to the end of the string, and then spin it around above your head. If we were to increase the speed at which we rotate our hand, we increase the velocity of the yo-yo - it is spinning faster. As it spins faster, it also changes direction faster. The acceleration increases. Now let's think about the bottom of the equation: the radius. If we halve the length of the yo-yo string (bring the yo-yo closer to us), we make the yo-yo's velocity greater. Again, it moves faster, which increases the acceleration. If we make the string longer again, this decreases the acceleration. We now understand why the relationship between the radius and the acceleration is an inverse relationship - as we decrease the radius, the acceleration increases, and visa versa.

Situation: Hazel is at the circus with her children and they are watching the performers ride motorcycles in a circular cage. They notice that the motorcycles are going different speeds and are curious as to why. They observe that Cage A is larger than Cage B and has a larger radius while Cage B is smaller than Cage A and has a smaller radius.

Question: In which cage will the motorcycle be accelerating faster?

Situation: Hazel is at the circus with her children and they are watching the performers ride motorcycles in a circular cage. They notice that the motorcycles are going different speeds and are curious as to why. They observe that Cage A is larger than Cage B and has a larger radius while Cage B is smaller than Cage A and has a smaller radius.

Question: In which cage will the motorcycle be accelerating slower?

Situation: Hazel is at the circus with her children and they are watching the performers ride motorcycles in a circular cage. They notice that the motorcycles are going different speeds and are curious as to why. They observe that Cage A is larger than Cage B and has a larger radius while Cage B is smaller than Cage A and has a smaller radius.

Question: Will the motorcycle in Cage A be accelerating faster or slower than the motorcycle in Cage B?

Situation: Hazel is at the circus with her children and they are watching the performers ride motorcycles in a circular cage. They notice that the motorcycles are going different speeds and are curious as to why. They observe that Cage A is larger than Cage B and has a larger radius while Cage B is smaller than Cage A and has a smaller radius.

Question: Will the motorcycle in Cage B be accelerating faster or slower than the motorcycle in Cage B?

Situation: Hazel is at the circus with her children and they are watching the performers ride motorcycles in a circular cage. They notice that the motorcycles are going different speeds and are curious as to why. They observe that Cage A is larger than Cage B and has a larger radius while Cage B is smaller than Cage A and has a smaller radius.

Question: If the radius of Cage A is decreased, will the motorcycle accelerate faster or slower?

Situation: Hazel is at the circus with her children and they are watching the performers ride motorcycles in a circular cage. They notice that the motorcycles are going different speeds and are curious as to why. They observe that Cage A is larger than Cage B and has a larger radius while Cage B is smaller than Cage A and has a smaller radius.

Question: If the radius of Cage B is increased, will the motorcycle accelerate faster or slower?