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).
please help me!
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
LOL, it takes time, it is almost midnight, and I have to work tomorrow.
i got it! thank you!! =)
To solve this problem, we need to use the formulas for tangential speed, total kinetic energy, moment of inertia, and rotational kinetic energy. Let's go step by step:
(a) The tangential speed of an object rotating around the z-axis can be found using the formula v = rω, where v is the tangential speed, r is the perpendicular distance from the axis of rotation, and ω is the angular speed.
For each object, the tangential speed can be calculated as follows:
- Object 1: v1 = r1 * ω = 2.20 m * 6.12 rad/s
- Object 2: v2 = r2 * ω = 15.20 m * 6.12 rad/s
- Object 3: v3 = r3 * ω = 3.15 m * 6.12 rad/s
(b) The total kinetic energy of the system can be calculated using the formula KE = ½m1v1^2 + ½m2v2^2 + ½m3v3^2. Simply substitute the given values into this equation to find the answer.
(c) The moment of inertia of the system can be found by summing the individual moments of inertia. The moment of inertia for a point mass rotating around an axis at a distance r is given by I = mr^2. Therefore, the total moment of inertia for the system is I = m1r1^2 + m2r2^2 + m3r3^2.
(d) The rotational kinetic energy of the system can be calculated using the formula KER = ½Iω^2. Substitute the moment of inertia obtained in part (c) and the given value of angular speed ω to find the rotational kinetic energy.
Remember to use the appropriate units when performing calculations.