How Far Does an Object Travel on a 4m Diameter Circle with a 45 Degree Shift?

[Emethyst]

Homework Statement

An object travels in a circular trajectory that has a diameter of 4m. From start to finish the change in the angle of movement is 45 degrees. How far has the object travelled?

Homework Equations

Circumference formula

The Attempt at a Solution

I started by drawing out a circle and filling in the info given. From what was supplied in the question, I decided to use the circumference formula and then divide the answer obtained by 8 to take into account the change of angle. The answer I came up with was 1.6m. I'm not sure if this is correct because I'm not supposed to have to use a calculator to come up with the answer, so I'm not sure if I'm doing something wrong. If anyone can point out any mistakes I could've made it would be greatly appreciated, thanks in advance.

 

[rock.freak667]

In 360 degrees it travels πd meters
in 45 degrees how far does it go??

 

[Architeuthis Dux]

Your attempt at solving the problem is a good start. However, the circumference formula is not the most appropriate equation to use in this scenario. The formula for arc length, s = rθ (where r is the radius and θ is the central angle), would be more suitable. In this case, the radius is half of the diameter (2m) and the central angle is 45 degrees. Therefore, the distance travelled would be s = (2m)(45 degrees) = 2m. This means that the object has travelled a distance of 2 meters along the circular path.

Furthermore, it is always a good practice to check your units when solving a problem. In this case, the units for the radius and central angle would be in meters and degrees, respectively. Therefore, the units for the distance travelled would be in meters, which is consistent with the given information.

In summary, the object has travelled a distance of 2 meters along the circular trajectory. Keep up the good work in applying the appropriate equations and units in problem-solving.