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?
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills