Question

Physics Genius! please let me!
Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 6.12 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 6.36 kg and r1 = 2.20 m, (2) m2 = 3.92 kg and r2 = 15.20 m, (3) m3 = 2.91 kg and r3 = 3.15 m.

(a) Find the tangential speed of each object.

(b) Determine the total kinetic energy of this system using the expression KE = ½m1v12 + ½m2v22 + ½m3v32.

(c) Obtain the moment of inertia of the system.

(d) Find the rotational kinetic energy of the system using the relation KER = ½Iω2 to verify that the answer is the same as the answer to (b).

Answer 1

please help me!

Answer 2

v = omega r
1. 6.12 * 2.20 = 13.464 m/s
2. 6.12 * 15.2 = 93.024
3. 6.12 * 3.15 = 19.278

(1/2) m v^2
1. .5 * 6.36 * 13.464^2 = 577 Joules
2. you can do the next two
3.
add them

I = m r^2
1. 6.36 (2.2)^2 = 30.8
2. you can do
3. you can do
add them for total I

Ke = (1/2) I omega^2
you just use total I and 6.12^2

I did not do totals so will just check object 1
.5 * 30.8 * 6.12^2 = 577 Joules, as we got up above using .5 m v^2

Answer 3

LOL, it takes time, it is almost midnight, and I have to work tomorrow.

Answer 4

i got it! thank you!! =)