Torque on a compound wheel

In summary, the wheel about the axle has a net torque of 6.200116816 N when the forces acting on it are 13 N, 28 N, and 13 N, acting at a 40◦ below the horizontal angle.
  • #1
Elbobo
145
0
(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.
 
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  • #2
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.
 

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  • #3
Elbobo said:
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?
 
  • #4
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...
 
  • #5
Looks fine to me. (Depending upon how fussy your online system is, you might need to use the correct number of significant figures.)
 
  • #6
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
 

1. What is torque on a compound wheel?

Torque on a compound wheel refers to the rotational force that is applied to the wheel. It is a combination of the torque applied to each individual component of the wheel.

2. How is torque calculated on a compound wheel?

To calculate the torque on a compound wheel, you need to first determine the torque on each individual component of the wheel using the formula T = r x F, where T is torque, r is the radius from the center of rotation to the point where the force is applied, and F is the force applied. Then, you can add the torques of each component together to get the total torque on the compound wheel.

3. What factors affect torque on a compound wheel?

There are several factors that can affect the torque on a compound wheel, including the magnitude and direction of the applied force, the distance from the center of rotation to where the force is applied, and the mass and distribution of mass of the wheel's components.

4. How does torque affect the motion of a compound wheel?

The torque on a compound wheel determines its rotational motion. If the torque is greater than the resistance to rotation, the wheel will accelerate in the direction of the applied force. If the torque is equal to the resistance to rotation, the wheel will maintain a constant speed. And if the torque is less than the resistance to rotation, the wheel will decelerate.

5. What are some real-world applications of torque on a compound wheel?

Torque on a compound wheel is relevant in many real-world applications, such as bicycle wheels, car wheels, and machinery with rotating parts. Understanding torque is important in designing and optimizing these systems for efficient and safe operation.

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