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Learning objectives

By the end of this section, you will be able to:

  • Understand the relationship between force, mass, and acceleration.
  • Study the turning effect of force.
  • Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 4.D.1.1 The student is able to describe a representation and use it to analyze a situation in which several forces exerted on a rotating system of rigidly connected objects change the angular velocity and angular momentum of the system. (S.P. 1.2, 1.4)
  • 4.D.1.2 The student is able to plan data collection strategies designed to establish that torque, angular velocity, angular acceleration, and angular momentum can be predicted accurately when the variables are treated as being clockwise or counterclockwise with respect to a well-defined axis of rotation, and refine the research question based on the examination of data. (S.P. 3.2, 4.1, 5.1, 5.3)
  • 5.E.2.1 The student is able to describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a fixed set of extended objects and point masses. (S.P. 2.2)

If you have ever spun a bike wheel or pushed a merry-go-round, you know that force is needed to change angular velocity as seen in [link] . In fact, your intuition is reliable in predicting many of the factors that are involved. For example, we know that a door opens slowly if we push too close to its hinges. Furthermore, we know that the more massive the door, the more slowly it opens. The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration; another implication is that angular acceleration is inversely proportional to mass. These relationships should seem very similar to the familiar relationships among force, mass, and acceleration embodied in Newton's second law of motion. There are, in fact, precise rotational analogs to both force and mass.

The given figure shows a bike tire being pulled by a hand with a force F backward indicated by a red horizontal arrow that produces an angular acceleration alpha indicated by a curved yellow arrow in counter-clockwise direction.
Force is required to spin the bike wheel. The greater the force, the greater the angular acceleration produced. The more massive the wheel, the smaller the angular acceleration. If you push on a spoke closer to the axle, the angular acceleration will be smaller.

To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force F size 12{F} {} on a point mass m size 12{m} {} that is at a distance r size 12{r} {} from a pivot point, as shown in [link] . Because the force is perpendicular to r size 12{r} {} , an acceleration a = F m size 12{a= { {F} over {m} } } {} is obtained in the direction of F size 12{F} {} . We can rearrange this equation such that F = ma size 12{F= ital "ma"} {} and then look for ways to relate this expression to expressions for rotational quantities. We note that a = size 12{a=rα} {} , and we substitute this expression into F = ma size 12{F= ital "ma"} {} , yielding

F = mr α . size 12{F= ital "mr"α"."} {}

Recall that torque    is the turning effectiveness of a force. In this case, because F size 12{"F"} {} is perpendicular to r size 12{r} {} , torque is simply τ = Fr size 12{τ=rα} {} . So, if we multiply both sides of the equation above by r size 12{r} {} , we get torque on the left-hand side. That is,

Questions & Answers

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Muhammad Reply
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Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
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Ziyad Reply
How bacteria create energy to survive?
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Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
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Muhamad
they make spores
Louisiaste
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the significance of food webs for disease transmission
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food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
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Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
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faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
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Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
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Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
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en français
Adama
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ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
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skin
Asiina
skin,Oral,Nasal,GIt
Sadik
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all
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by fussion
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part of a tissue or an organ being wounded or bruised.
Wilfred
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Micheal Reply
Binomial nomenclature
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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