How Do You Calculate Net Torque on a Compound Wheel?

[Elbobo]

(sorry about another topic but this week's HW is hard @_@)

Homework Statement

A circular-shaped object has an inner radius
of 6 cm and an outer radius of 22 cm. Three
forces (acting perpendicular to the axis of
rotation) of magnitudes 13 N, 28 N, and 13 N
act on the object, as shown. The force of
magnitude 28 N acts 40◦ below the horizontal.

Find the magnitude of the net torque on
the wheel about the axle through the center
of the object. Answer in units of N · m.

Homework Equations

Torque = Fd sin (th)

The Attempt at a Solution

I ignored the mass because the teacher didn't mention anything about reading over the moment of intertia section in our textbook, but I think she was wrong... Anyway:

Clockwise as the positive direction.

Net Torque = (13 * 0.28) + (13 * 0.28) - (28 * 0.06 sin 40)
Net torque = 6.200116816 m*N (WRONG)

T_T I tried reading the section, but it gave me an equation (Net Torque = Moment of intertia * angular acceleration) I couldn't do anything with, as I didn't know how to solve for the angular acceleration.

 

[Elbobo]

Oh the mass on the picture was 10 kg, if that even matters.

I'll post a pic if it's needed.

EDIT: Oops, now that I read that over, a picture is required.

 

[Doc Al]

I ignored the mass because the teacher didn't mention anything about reading over the moment of intertia section in our textbook, but I think she was wrong... Anyway:

Since the question only asks for the net torque, not the resulting angular acceleration, you don't have to worry about moment of inertia.

Clockwise as the positive direction.

Net Torque = (13 * 0.28) + (13 * 0.28) - (28 * 0.06 sin 40)
Net torque = 6.200116816 m*N (WRONG)

The outer radius is 22 cm, not 28 cm (don't add the inner and outer radii). Does the angle that the 28 N force makes with the horizontal affect the torque it creates around the axis?

 

[Elbobo]

OK so the angle shouldn't even matter since it's already perpendicular to the radius...

So then I did:

(13 * 0.22) + (13 * 0.22) - (28 * 0.06) = 4.04 m*N

which is still wrong...

 

[Doc Al]

Looks fine to me. (Depending upon how fussy your online system is, you might need to use the correct number of significant figures.)

 

[Elbobo]

my online system accepts the most possible digits as can be, which is 4.04

two other people I've asked also approved of 4.04 X_X

some of my friends said that this week's HW won't accept the obviously right answer, i.e. glitch/mistake in the system. i hope it's that