A gob of clay, mass 217 g, falls from rest a distance 50 cm before striking and sticking to the edge of a wheel free to rotate about a horizontal axis through its center (Fig. 10-38). The wheel can be approximated as a solid disk of mass 49 kg and radius 84 cm. What is the angular speed of the wheel with the gob of clay attached?

Question

A gob of clay, mass 217 g, falls from rest a distance 50 cm before striking and sticking to the edge of a wheel free to rotate about a horizontal axis through its center (Fig. 10-38). The wheel can be approximated as a solid disk of mass 49 kg and radius 84 cm. What is the angular speed of the wheel with the gob of clay attached? 
(Answer: 0.0327rad/s)

Answer is provided above. Please show all work on how to get the answer.

Anonymous · Answer

m = 0.217kg
h = 0.5m
M = 49kg
r = 0.84m

mvr = Iw
1/2mv^2 = mgh
v = sqrt[2gh]
v = sqrt[2 * 9.8m/s^2 * 0.5m]
v = 3.1m/s

w = mvr / I
w = mvr / 1/2Mr^2
w = 2msqrt[2gh] / Mr
w = 2(0.217kg)(3.1m/s) / (49kg * 0.84m)
w = 0.033rad/s