Question

1) A point on the rim of a 0.15-m-radius rotating disk has a centripetal acceleration of 4.0 m/s2. What is the angular speed of a point 0.075 m from the center of the disk? 2) A point on the rim of a 0.30-m-radius fan blade has centripetal acceleration of 0.35 m/s2. Find the centripetal acceleration of a point 0.040 m from the center of the same wheel. 3) Masses are distributed in the xy-plane as follows: 2.0 kg at (0.0, 0.0) m, 6.0 kg at (2.0, 0.0) m, and 4.0 kg at (2.0,3.0) m. What is the x-coordinate of the center of gravity of this system of masses?

Answer 1

1) a = rw^2
4 = 0.15*w^2
w = 5.164 s^-1
angular speed = 5.164 s^-1

2) a = rw^2
w, angular velocity, is the same for all points
So, a is directly proportional to r

a = 0.35*0.04/0.3
= 0.0467 m/s^2

3) x-coordinate = 2*0 + 6*2 + 4*2 /(2+4+6)
= 20/12
= 1.67 m