QUIZ 8

1. Three point masses of m₁ = 2kg, m₂ = 3kg, and m₃ = 5kg, are located on a line as shown. Find the center of mass of the three-point system.

Solution. Choose  the origin of the coordinate system at 2-kg  mass. We find CM form                  xCM = (x1m1 + x2m2 + x3m3)/(m1 + m2 + m3)                          = [(2kg)(0) + (3kg)(4cm) + (5kg)(4cm + 6cm)]/(2kg + 3kg + 5kg)                           = 6.2cm (to the right of the 2-kg point).

2. A 50-cm wheel accelerates uniformly from rest to 5m/s in 4 second. What is the angular acceleration of the wheel?

Solution. we find the linear acceleration of the wheel from

                 v = v₀ + at;

                 (5m/s) = 0 + a(4s), which gives a = 1.25m/s².

              We find the angular acceleration from

                  a = a/r = (1.25m/s²)/(0.5m/2) = 5.0rad/s².