Torque is the analog of force and moment of inertia is the analog of mass. Force and mass are physical quantities that depend on only one factor. For example, mass is related solely to the numbers of atoms of various types in an object. Are torque and moment of inertia similarly simple?
No. Torque depends on three factors: force magnitude, force direction, and point of application. Moment of inertia depends on both mass and its distribution relative to the axis of rotation. So, while the analogies are precise, these rotational quantities depend on more factors.
The farther the force is applied from the pivot, the greater is the angular acceleration; angular acceleration is inversely proportional to mass.
If we exert a force
on a point mass
that is at a distance
from a pivot point and because the force is perpendicular to
, an acceleration
is obtained in the direction of
. We can rearrange this equation such that
and then look for ways to relate this expression to expressions for rotational quantities. We note that
, and we substitute this expression into
, yielding
Torque is the turning effectiveness of a force. In this case, because
is perpendicular to
, torque is simply
. If we multiply both sides of the equation above by
, we get torque on the left-hand side. That is,
or
The moment of inertia
of an object is the sum of
for all the point masses of which it is composed. That is,
The general relationship among torque, moment of inertia, and angular acceleration is
or
Conceptual questions
The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is
. Why is this moment of inertia greater than it would be if you spun a point mass
at the location of the center of mass of the rod (at
)? (That would be
.)
Why is the moment of inertia of a hoop that has a mass
and a radius
greater than the moment of inertia of a disk that has the same mass and radius? Why is the moment of inertia of a spherical shell that has a mass
and a radius
greater than that of a solid sphere that has the same mass and radius?
While reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionless ramp (with the same slope angle). In which case does it reach a greater height, and why?
This problem considers additional aspects of example
Calculating the Effect of Mass Distribution on a Merry-Go-Round . (a) How long does it take the father to give the merry-go-round an angular velocity of 1.50 rad/s? (b) How many revolutions must he go through to generate this velocity? (c) If he exerts a slowing force of 300 N at a radius of 1.35 m, how long would it take him to stop them?
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
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
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
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 ❣️
_Adnan
define infection ,prevention and control
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