Now let’s apply this problem-solving strategy to a few specific examples.
A spinning bicycle wheel
A bicycle mechanic mounts a bicycle on the repair stand and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. (a) Calculate the average angular acceleration in
. (b) If she now hits the brakes, causing an angular acceleration of −87.3
, how long does it take the wheel to stop?
Strategy
The average angular acceleration can be found directly from its definition
because the final angular velocity and time are given. We see that
and
is 5.00 s. For part (b), we know the angular acceleration and the initial angular velocity. We can find the stopping time by using the definition of average angular acceleration and solving for
, yielding
Solution
Entering known information into the definition of angular acceleration, we get
Because
is in revolutions per minute (rpm) and we want the standard units of
for angular acceleration, we need to convert from rpm to rad/s:
Entering this quantity into the expression for
, we get
Here the angular velocity decreases from 26.2 rad/s (250 rpm) to zero, so that
is −26.2 rad/s, and
is given to be –87.3
. Thus,
Significance
Note that the angular acceleration as the mechanic spins the wheel is small and positive; it takes 5 s to produce an appreciable angular velocity. When she hits the brake, the angular acceleration is large and negative. The angular velocity quickly goes to zero.
Check Your Understanding The fan blades on a turbofan jet engine (shown below) accelerate from rest up to a rotation rate of 40.0 rev/s in 20 s. The increase in angular velocity of the fan is constant in time. (The GE90-110B1 turbofan engine mounted on a Boeing 777, as shown, is currently the largest turbofan engine in the world, capable of thrusts of 330–510 kN.)
(a) What is the average angular acceleration?
(b) What is the instantaneous angular acceleration at any time during the first 20 s?
a.
,
; b. Since the angular velocity increases linearly, there has to be a constant acceleration throughout the indicated time. Therefore, the instantaneous angular acceleration at any time is the solution to
.
A wind turbine (
[link] ) in a wind farm is being shut down for maintenance. It takes 30 s for the turbine to go from its operating angular velocity to a complete stop in which the angular velocity function is
. If the turbine is rotating counterclockwise looking into the page, (a) what are the directions of the angular velocity and acceleration vectors? (b) What is the average angular acceleration? (c) What is the instantaneous angular acceleration at
Strategy
We are given the rotational sense of the turbine, which is counterclockwise in the plane of the page. Using the right hand rule (
[link] ), we can establish the directions of the angular velocity and acceleration vectors.
We calculate the initial and final angular velocities to get the average angular acceleration. We establish the sign of the angular acceleration from the results in (a).
We are given the functional form of the angular velocity, so we can find the functional form of the angular acceleration function by taking its derivative with respect to time.
Solution
Since the turbine is rotating counterclockwise, angular velocity
points out of the page. But since the angular velocity is decreasing, the angular acceleration
points into the page, in the opposite sense to the angular velocity.
The initial angular velocity of the turbine, setting
. The final angular velocity is zero, so the average angular acceleration is
Taking the derivative of the angular velocity with respect to time gives
Significance
We found from the calculations in (a) and (b) that the angular acceleration
and the average angular acceleration
are negative. The turbine has an angular acceleration in the opposite sense to its angular velocity.
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