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  • 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.

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,

rF = mr 2 α size 12{ ital "rF"= ital "mr" rSup { size 8{2} } α} {}

or

τ = mr 2 α. size 12{τ= ital "mr" rSup { size 8{2} } α.} {}

This last equation is the rotational analog of Newton’s second law ( F = ma size 12{F= ital "ma"} {} ), where torque is analogous to force, angular acceleration is analogous to translational acceleration, and mr 2 size 12{ ital "mr" rSup { size 8{2} } } {} is analogous to mass (or inertia). The quantity mr 2 size 12{ ital "mr" rSup { size 8{2} } } {} is called the rotational inertia    or moment of inertia    of a point mass m size 12{m} {} a distance r size 12{r} {} from the center of rotation.

The given figure shows an object of mass m, kept on a horizontal frictionless table, attached to a pivot point, which is in the center of the table, by a cord that supplies centripetal force. A force F is applied to the object perpendicular to the radius r, which is indicated by a red arrow tangential to the circle, causing the object to move in counterclockwise direcion.
An object is supported by a horizontal frictionless table and is attached to a pivot point by a cord that supplies centripetal force. A force F size 12{F} {} is applied to the object perpendicular to the radius r size 12{r} {} , causing it to accelerate about the pivot point. The force is kept perpendicular to r size 12{r} {} .

Making connections: rotational motion dynamics

Dynamics for rotational motion is completely analogous to linear or translational dynamics. Dynamics is concerned with force and mass and their effects on motion. For rotational motion, we will find direct analogs to force and mass that behave just as we would expect from our earlier experiences.

Questions & Answers

how can we find absolute uncertainty
ayesha Reply
it what?
Luke
in physics
ayesha
the basic formula is uncertainty in momentum multiplied buy uncertainty In position is greater than or equal to 4×pi/2. same formula for energy and time
Luke
I have this one question can you please look it up it's 9702/22/O/N/17 Question 1 B 3
ayesha
what
uma
would you like physics?
Suthar
yes
farooq
how do I unlock the MCQ and the Essay?
Ojeh Reply
what is the dimension of strain
Joy Reply
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
Cyclone Reply
hi
Agboro
hiii
Chandan
Hi
Sahim
hi
Jeff
hey
Priscilla
sup guys
Bile
Hy
Kulsum
What is unit of watt?
Kulsum
watt is the unit of power
Rahul
p=f.v
Rahul
watt can also be expressed as Nm/s
Rahul
what s i unit of mass
Maxamed
SI unit of mass is Kg(kilogram).
Robel
what is formula of distance
Maxamed
Formula for for the falling body with initial velocity is:v^2=v(initial)^2+2*g*h
Mateo
i can't understand
Maxamed
we can't do this calculation without knowing the height of the initial position of the particle
Chathu
sorry but no more in science
Imoreh
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
Victor Reply
50 N... (50 *1.732)N
Sahim
Plz cheak the ans and give reply..
Sahim
Is earth is an inertial frame?
Sahim Reply
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Sahim
thanks
Irungu
Most welcome
Sahim
Hey.. I've a question.
Sahim Reply
Is earth inertia frame?
Sahim
only the center
Shii
What is an abucus?
Irungu
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
prakash Reply
someone please give answer to this.
prakash
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Ebenezer Reply
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
El
so solve it
Ebenezer
please
Ebenezer
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
Oluwatola Reply
what is cesium atoms?
prakash Reply
The atoms which form the element Cesium are known as Cesium atoms.
Naman
A material that combines with and removes trace gases from vacuum tubes.
Shankar
what is difference between entropy and heat capacity
Varun
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
Chathu
I want learn physics
Vinodhini Reply
sir how to understanding clearly
Vinodhini
try to imagine everything you study in 3d
revolutionary
pls give me one title
Vinodhini
displacement acceleration how understand
Vinodhini
vernier caliper usage practically
Vinodhini
karthik sir is there
Vinodhini
what are the solution to all the exercise..?
What is realm
Vinodhini Reply
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
revolutionary
How to understand physics
Vinodhini Reply
i like physics very much
Vinodhini
i want know physics practically where used in daily life
Vinodhini
I want to teach physics very interesting to studentd
Vinodhini
how can you build interest in physics
Prince
by reading it
Austin
understanding difficult
Vinodhini
vinodhini mam, physics is used in our day to day life in all events..... everything happening around us can be explained in the base of physics..... saying simple stories happening in our daily life and relating it to physics and questioning students about how or why its happening like that can make
revolutionary
your class more interesting
revolutionary
anything send about physics daily life
Vinodhini
How to understand easily
Vinodhini
check out "LMES" youtube channel
revolutionary
even when you see this message in your phone...it works accord to a physics principle. you touch screen works based on physics, your internet works based on physics, etc....... check out google and search for it
revolutionary
what is mean by Newtonian principle of Relativity? definition and explanation with example
revolutionary Reply
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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