Rotational Inertia of Irregular Disk

[Kyle8624]

Homework Statement

an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the following method. A circular disk of mass 0.500 kg and radius 2.00 cm is glued to the plate, with its center aligned with point O (Fig. 10-42b). A string is wrapped around the edge of the disk the way a string is wrapped around a top. Then the string is pulled for 5.00 s. As a result, the disk and plate are rotated by a constant force of 0.400 N that is applied by the string tangentially to the edge of the disk. The resulting angular speed is 114 rad/s. What is the rotational inertia of the plate about the axle?

Homework Equations

alpha = omega/t
torque = I(alpha)
torque = r(F)

The Attempt at a Solution

I searched the forums and found a year old solution, but it still wasn't detailed enough for me to get the right answer. I started by finding alpha, which was 22.8 rad/s^2. From there, I don't know how to get the I value of the plate, although I can find I value for the disk using

T = rF
= 0.02(0.4)
= 0.008 Nm

T = I(alpha)
I = 0.008/22.8
= 0.0035088

Then I get stuck and don't know how to relate the disk and plate together to find the I for the plate.

 

[tiny-tim]

Welcome to PF!

Hi Kyle8624! Welcome to PF!

(have an alpha: α and an omega: ω and a tau: τ and try using the X² icon just above the Reply box )

I_total = I_disc + I_plate

 

[Kyle8624]

as for the question, I think I calculated the I for the disk, but I don't know how to get the total rotational inertia.

 

[tiny-tim]

Hi Kyle8624!

(just got up :zzz: …)

as for the question, I think I calculated the I for the disk, but I don't know how to get the total rotational inertia.

You get I_total from τ/α, and then you get I_plate from I_total = I_disc + I_plate

 

[Kyle8624]

hi again : D

thanks for all of the help so far, but I think I'm missing some concept here. How do you get I_total if the radius of the plate is uneven.

 

[tiny-tim]

You get I_total from τ/α.