<< Chapter < Page Chapter >> Page >

Torque

We know that torque is equal to

T = r * Fp

where

  • T represents torque
  • r represents the distance from the center of the wheel to the point where the perpendicular force is applied
  • Fp represents the perpendicular force

Arc length

We also know that the arc length is given by

s = r * A

where

  • s represents the arc length
  • r represents the distance from the center of the wheel to the point where the perpendicular force is applied as before
  • A represents the angle of displacement measured in radians

Through substitution

W = Fp * s, or

W = (T/r)*r*A, or

The work done by a constant torque is given by the equation shown in Figure 2.

Figure 2 . Work done by constant torque.

W = T*A

where

  • W represents the work done by a constant torque
  • T represents the constant torque
  • A represents the angle of displacement measured in radians resulting from the application of the constant torque

Work can be either positive or negative. If the torque and the angular displacement have the same sign, the work is positive.Otherwise, the work is negative.

Power

As in the translational case, power is a measure of the work done per unit of time. If we divide both sides of the above equation by time, we get

(W/t) = T*(A/t)

where

  • W/t = work per second or power
  • A is the angular displacement in radians
  • t is time in seconds
  • A/t is the displacement in radians per second, which we recognize as angular velocity

Thus, the power generated or consumed by applying a constant torque is given by the equation shown in Figure 3 .

Figure 3 . Power generated or consumed by a constant torque.

P = T*w

where

  • P represents power in watts (joules per second or newton-meters per second)
  • T represents torque in newton meters
  • w represents angular velocity in radians per second

Variable torque

A torque doesn't have to be constant to do work. In fact, the torque generated by the user with the starter rope on the power mower discussed in theprevious section probably isn't constant.

However, if the torque is not constant, you cannot use the equations developed in the previous section to compute the work done by the torque.

Maybe you can use calculus

If the torque as a function of time can be described by a function that you can integrate using integral calculus, you can use calculus to compute the workdone by the torque. However, in the real word, this is probably rarely the case.

Maybe you can use a computer

If you are in the business of computing work done by a variable torque, the most likely case is that you will have equipment that allows you to sample thetorque and displacement values at uniform intervals of time and to save the values of the samples for digital processing. Then you can use any one ofseveral digital methods to approximately integrate the product of the torque function and the displacement function.

Example scenario

I once visited a factory where mirrors were made. At one of the stations on the manufacturing line, a person used a large horizontal grinding wheel to grinda bevel on the edge of the mirror.

Assume that the grinding wheel is a uniform disk with:

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Accessible physics concepts for blind students' conversation and receive update notifications?

Ask