1. Angular Kinetics: Torques
Pages
4/16/2019
Dr. Sasho MacKenzie - HK 376

2. What is a Torque () A torque is the angular result of a force.
It is the turning effect produced by a force.
A torque occurs about an axis or a point of rotation.
Another term for torque is moment.
Moment and torque are synonymous and will be used interchangeably throughout the course
4/16/2019
Dr. Sasho MacKenzie - HK 376

3. Calculating the Torque produced by a Force
Torque = Force x Moment arm
The torque produced by a force is equal to the magnitude of the force acting perpendicular to the moment arm (r) multiplied by the length of the moment arm.
Where the moment arm is the perpendicular distance from the line of action of the force to the point of rotation.
4/16/2019
Dr. Sasho MacKenzie - HK 376

4. An Example
Viewed from the ceiling, a person pulls on a door knob with 100 N of force. The distance from the hinges of the door to the door knob is 0.6 m. We can determine the torque produced on the door about its hinges.
0.6 m
Hinges
100 N
Torque = Fr = (100 N)(0.6 m) = Nm
4/16/2019
Dr. Sasho MacKenzie - HK 376

5. Where do Torques exist?
Virtually every force that we deal with produces a torque.
All of the body’s muscles are attached at a distance from the joint centers; therefore, they all produce torques.
The spin on a ball is the result of a torque.
Gymnasts use torques to perform flips and twists.
Wheels turn because of torques.
4/16/2019
Dr. Sasho MacKenzie - HK 376

6. Defining the Moment Arm (r)
The moment arm is the perpendicular distance from the line of action of the force to the point of rotation.
Only when the force acts at 90 to the object will the moment arm be the distance from the point of rotation along the length of the object to the force.
The 90 angle is formed between the force and the moment arm, NOT the object and the moment arm, and NOT the object and the force.
4/16/2019
Dr. Sasho MacKenzie - HK 376

7. Drawing the Moment Arm (r)F 1.
Moment Arm (r) 2.
Moment Arm (r)
Moment Arm (r) 3.
4/16/2019
Dr. Sasho MacKenzie - HK 376

8. Calculating Moment Arm LengthF
30
10 m A r
5 m
Sin 30 = Opposite = r
Hypotenuse 10
r = Sin 30 * = (0.5) * (10) = 5 m
If the the force F was 200 N, then we could figure out the torque produced about the point of rotation A.
Torque = Fr = (200 N) (5 m) = Nm
4/16/2019
Dr. Sasho MacKenzie - HK 376

9. Another Very Important Method for Calculating Torque
The same understanding applies to both methods.
There is nothing new to learn in understanding the second method.
Instead of finding the moment arm perpendicular to the force, we find the component of the force that is perpendicular to the existing moment arm.
A force component that passes through the point of rotation produces no torque.
4/16/2019
Dr. Sasho MacKenzie - HK 376

10. Calculating Perpendicular Force
Parallel Component (Fx)
produces no torque because it passes through point A A
30
10 m
F = 200 N
Perpendicular Component (Fy) of force produces all the torque
30
Sin 30 = Opposite = Fy = Fy
Hypotenuse F
Fy = Sin 30 * 200 N = N
Since we know our moment arm is 10 m, we can figure out the torque produced by the Force.
Torque = Fr (100 N) (10 m) = Nm
4/16/2019
Dr. Sasho MacKenzie - HK 376

11. Torque Notables
Torque is a vector whose direction is determined using the right hand rule in the same way as angular velocity.
Counter-clockwise is positive and clockwise is negative.
If a torque exists, then a force must have produced it.
Resolving forces into components is a huge part of determining torques (Trigonometry).
4/16/2019
Dr. Sasho MacKenzie - HK 376

12. Examples: What is the Torque about Point A1.
Torque = A
100 N
5 m
6 m 2.
Torque =
600 Nm
0 Nm A
100 N
5 m
6 m 3.
Torque =
30
100 N
2 m A
Torque = 4.
-200 N m
-500 N m
4/16/2019
Dr. Sasho MacKenzie - HK 376