Question

The location of the center of mass of the partially eaten, 12-inch diameter pizza shown in the figure (Figure 1) is Xcm = - 1.5 in

and Ycm = -1.5 in .

Answer 1

The center of mass of a slice of pizza can be found by taking the average of the x and y coordinates of the center of each slice.

Step-by-step explanation:

The center of mass of a slice of pizza that was cut into eight equal slices can be found by taking the average of the x and y coordinates of the center of each slice. The x coordinate of the center of mass can be found using the formula Xcm = -R/π * (cos(α/2) + cos(3α/2) + cos(5α/2) + cos(7α/2)), where R is the radius of the pizza and α is the angle between each slice. Similarly, the y coordinate of the center of mass can be found using the formula Ycm = R/π * (sin(α/2) + sin(3α/2) + sin(5α/2) + sin(7α/2)). Plugging in the values for the given pizza, with a diameter of 12 inches, the center of mass can be calculated as Xcm = -1.5 in and Ycm = -1.5 in.

Answer 2

The center of mass of a slice of pizza can be found by taking the average of the x and y coordinates of the center of each slice.

The center of mass of a slice of pizza can be found by taking the average of the x and y coordinates of the center of each slice.

The angle between each slice α = 360°/8

The angle between each slice α =45°

The diameter of the pizza is given, so the radius (R) is half of the diameter:

R = 12 / 2

R = 6 inches.

The x coordinate of the center of mass can be found using the formula:

Xcm = -R/π * (cos(α/2) + cos(3α/2) + cos(5α/2) + cos(7α/2)),

where R is the radius of the pizza and α is the angle between each slice.

The y coordinate of the center of mass can be found using the formula:

Ycm = R/π * (sin(α/2) + sin(3α/2) + sin(5α/2) + sin(7α/2)).

Therefore, the center of mass can be calculated as Xcm = -1.5 in and Ycm = -1.5 in.