Torque and Rotational Motion

In summary, the conversation discusses the calculation of the magnitude and direction of the angular acceleration of a uniform cylinder with a mass of 2.9 kg and forces applied at points F1 = 2.4 N, F2 = 3.9 N, F3 = 6.1 N, and F4 = 4.6 N. The radius at points R1 = 11.2 cm and R3 = 4.0 cm are also given. The formula used is Torque (net) = Inertia * Angular Acceleration, with Torque calculated as Force * Radius * sin(angle). The conversation also mentions the importance of considering the angle at which the force is applied in the calculation.
  • #1
Swagger
19
0
A uniform 2.9-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 2.4 N, F2 = 3.9 N, F3 = 6.1 N, and F4 = 4.6 N. Also, R1 = 11.2 cm and R3 = 4.0 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder. (see attachment)

I'm having a hard time with this one. I know that:
Torque (net) = Inertia * Angular Acceleration
and
Torque = Force * Radius

I've got:
T(F1)=0.2688 Nm
T(F2)=-0.4368 Nm
T(F3)=-0.0244 Nm
T(F4)=0 Nm

Tnet=-0.1924 Intertia=0.0181888
and the angular accerleration= -10.58 rad/s^2 (INCORRECT)

What am I doing wrong?
 

Attachments

  • prob09.gif
    prob09.gif
    5.5 KB · Views: 1,764
Physics news on Phys.org
  • #2
Swagger said:
A uniform 2.9-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 2.4 N, F2 = 3.9 N, F3 = 6.1 N, and F4 = 4.6 N. Also, R1 = 11.2 cm and R3 = 4.0 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder. (see attachment)

I'm having a hard time with this one. I know that:
Torque (net) = Inertia * Angular Acceleration
and
Torque = Force * Radius

I've got:
T(F1)=0.2688 Nm
T(F2)=-0.4368 Nm
T(F3)=-0.0244 Nm
T(F4)=0 Nm

Tnet=-0.1924 Intertia=0.0181888
and the angular accerleration= -10.58 rad/s^2 (INCORRECT)

What am I doing wrong?


I can't see the figure yet so I can't tell. But the torque is F times r times sin theta. That may (or may not, depending on what direction the forces are acting) explain a discrepancy.

Pat
 
  • #3
Swagger said:
A uniform 2.9-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 2.4 N, F2 = 3.9 N, F3 = 6.1 N, and F4 = 4.6 N. Also, R1 = 11.2 cm and R3 = 4.0 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder. (see attachment)
The diagram seems to show a single radius. What are R1 and R2? What's the radius of the cylinder?


I'm having a hard time with this one. I know that:
Torque (net) = Inertia * Angular Acceleration
OK.
and
Torque = Force * Radius
Don't forget the angle that the force is applied.

Torque = Force * Radius * sin(angle)
 
  • #4
Doc Al said:
Don't forget the angle that the force is applied.

Torque = Force * Radius * sin(angle)

All angles a 90deg, that would just be multiplying by 1, right? Also, is my F3 torque correct? I did .004 * 6.1
 
  • #5
nrqed said:
I can't see the figure yet so I can't tell. But the torque is F times r times sin theta. That may (or may not, depending on what direction the forces are acting) explain a discrepancy.

Pat

Your T(F3) is off by a factor of 10. That will probably do it.
 
  • #6
Swagger said:
All angles a 90deg, that would just be multiplying by 1, right?
Perhaps you are defining things differently, but only F1 and F2 are applied at 90 degrees to the radial line through the point of application.
 
  • #7
nrqed said:
Your T(F3) is off by a factor of 10. That will probably do it.


UGH! That was it...I got it. Thanks!
 
  • #8
Doc Al said:
The diagram seems to show a single radius. What are R1 and R2? What's the radius of the cylinder?



OK.

Don't forget the angle that the force is applied.

Torque = Force * Radius * sin(angle)

O k Doc I am just having trouble get my (T1), T(2)..., my numbers are off, so what is the formula for that?
 
  • #9
consemiu21 said:
O k Doc I am just having trouble get my (T1), T(2)..., my numbers are off, so what is the formula for that?
Formula for what? You just quoted the formula for finding the torque.

Show what you did.
 

1. What is torque and how does it differ from force?

Torque is a measure of the rotational force applied to an object. It differs from force in that it is specific to rotational motion, while force is a general term for any type of push or pull on an object.

2. How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied. The formula for torque is T = F x d, where T is torque, F is force, and d is distance.

3. What is the difference between clockwise and counterclockwise torque?

Clockwise torque causes an object to rotate in a clockwise direction, while counterclockwise torque causes an object to rotate in a counterclockwise direction. The direction of the force applied determines the direction of the torque.

4. What is the moment of inertia and how does it relate to torque?

The moment of inertia is a measure of an object's resistance to rotational motion. It is similar to mass in linear motion, as it determines how difficult it is to change an object's rotational speed. The greater the moment of inertia, the more torque is needed to cause a change in rotational motion.

5. What are some real-world applications of torque and rotational motion?

Torque and rotational motion are used in many everyday objects, such as bicycles, cars, and playground equipment. They are also important in industrial machinery and equipment, as well as in sports such as gymnastics and figure skating.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
11K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
4K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
27
Views
3K
Back
Top