## College Physics (4th Edition)

The center of mass of the leg is located at the point $(30~cm, 11.5~cm)$
We can find the coordinates of the center of mass of the 20-kg cylinder: $x = \frac{35~cm}{2} = 17.5~cm$ $y = 0$ We can find the coordinates of the center of mass of the 10-kg cylinder: $x = (35~cm)+(40~cm)~sin~30.0^{\circ} = 55~cm$ $y = (40~cm)~cos~30.0^{\circ} = 34.64~cm$ We can find the x-coordinate of the center of mass: $x_{com} = \frac{(20~kg)(17.5~cm)+(10~kg)(55~cm)}{20~kg+10~kg}$ $x_{com} = 30~cm$ We can find the y-coordinate of the center of mass: $y_{com} = \frac{(20~kg)(0)+(10~kg)(34.64~cm)}{20~kg+10~kg}$ $y_{com} = 11.5~cm$ The center of mass of the leg is located at the point $(30~cm, 11.5~cm)$.