where
is the initial angular velocity.
[link] is the rotational counterpart to the linear kinematics equation
. With
[link] , we can find the angular velocity of an object at any specified time
t given the initial angular velocity and the angular acceleration.
Let’s now do a similar treatment starting with the equation
. We rearrange it to obtain
and integrate both sides from initial to final values again, noting that the angular acceleration is constant and does not have a time dependence. However, this time, the angular velocity is not constant (in general), so we substitute in what we derived above:
where we have set
. Now we rearrange to obtain
[link] is the rotational counterpart to the linear kinematics equation found in
Motion Along a Straight Line for position as a function of time. This equation gives us the angular position of a rotating rigid body at any time
t given the initial conditions (initial angular position and initial angular velocity) and the angular acceleration.
We can find an equation that is independent of time by solving for
t in
[link] and substituting into
[link] .
[link] becomes
or
[link] through
[link] describe fixed-axis rotation for constant acceleration and are summarized in
[link] .
Kinematic equations
Angular displacement from average angular velocity
Angular velocity from angular acceleration
Angular displacement from angular velocity and angular acceleration
Angular velocity from angular displacement and angular acceleration
Applying the equations for rotational motion
Now we can apply the key kinematic relations for rotational motion to some simple examples to get a feel for how the equations can be applied to everyday situations.
Calculating the acceleration of a fishing reel
A deep-sea fisherman hooks a big fish that swims away from the boat, pulling the fishing line from his fishing reel. The whole system is initially at rest, and the fishing line unwinds from the reel at a radius of 4.50 cm from its axis of rotation. The reel is given an angular acceleration of
for 2.00 s (
[link] ).
(a) What is the final angular velocity of the reel after 2 s?
(b) How many revolutions does the reel make?
Strategy
Identify the knowns and compare with the kinematic equations for constant acceleration. Look for the appropriate equation that can be solved for the unknown, using the knowns given in the problem description.
Solution
We are given
and
t and want to determine
. The most straightforward equation to use is
, since all terms are known besides the unknown variable we are looking for. We are given that
(it starts from rest), so
We are asked to find the number of revolutions. Because
, we can find the number of revolutions by finding
in radians. We are given
and
t , and we know
is zero, so we can obtain
by using
Converting radians to revolutions gives
Significance
This example illustrates that relationships among rotational quantities are highly analogous to those among linear quantities. The answers to the questions are realistic. After unwinding for two seconds, the reel is found to spin at 220 rad/s, which is 2100 rpm. (No wonder reels sometimes make high-pitched sounds.)
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.
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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
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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