- #1

#### djsharpsound

at t = 0 a flywheel is rotating at 50 rpm. A motor gives it a constant acceleration of 0.5 rad/seconds(squared) until it reaches 100 rpm. The motor is then disconnected. How many revolutions are completed at t = 20 s ?

thanks

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- Thread starter djsharpsound
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- #1

at t = 0 a flywheel is rotating at 50 rpm. A motor gives it a constant acceleration of 0.5 rad/seconds(squared) until it reaches 100 rpm. The motor is then disconnected. How many revolutions are completed at t = 20 s ?

thanks

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- #2

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This kind of post has to go in "homework help".

In order to get help, you need to show something more than the bare problem.

What have you tried?

where are you stuck?

what equations you expect to be useful?

what happened when you tried them?

- #3

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Rotational kinematics deals with the motion of objects that are rotating or moving in a circular path. In this problem, we are given the initial and final angular velocities of a flywheel and asked to find the number of revolutions completed after a certain time.

To solve this problem, we can use the equation:

ωf = ωi + αt

Where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time.

Substituting the given values, we get:

100 rpm = 50 rpm + 0.5 rad/s^2 * t

Solving for t, we get:

t = 100 s

This means that after 100 seconds, the flywheel will reach 100 rpm. However, we are asked to find the number of revolutions completed after 20 seconds. To do this, we can use the equation:

θ = ωi * t + ½ * α * t^2

Where θ is the angle rotated, ωi is the initial angular velocity, α is the angular acceleration, and t is the time.

Substituting the values, we get:

θ = 50 rpm * 20 s + ½ * 0.5 rad/s^2 * (20 s)^2

Simplifying, we get:

θ = 1000 rad

To convert this to revolutions, we divide by 2π (since 2π radians is equal to one revolution):

θ = 1000 rad / 2π = 159.15 revolutions

Therefore, at t = 20 seconds, the flywheel will have completed approximately 159.15 revolutions. I hope this explanation helps you understand rotational kinematics better. Let me know if you have any further questions.

Rotational kinematics is the study of the motion of objects that rotate around a fixed axis. This includes concepts such as angular displacement, velocity, and acceleration.

Unlike linear kinematics, which deals with the motion of objects in a straight line, rotational kinematics deals with the motion of objects around a fixed axis. This leads to different equations and concepts, such as angular displacement and angular velocity, instead of linear displacement and linear velocity.

Angular velocity is a measure of how fast an object is rotating around a fixed axis. It is defined as the change in angular displacement over time and is measured in radians per second.

Rotational kinematics is used in a variety of real-world applications, such as understanding the motion of planets and other celestial bodies, designing and analyzing machinery and vehicles that involve rotation, and even in sports such as figure skating and gymnastics.

The three main equations of rotational kinematics are:

1. ω = ω_{0} + αt, where ω is the final angular velocity, ω_{0} is the initial angular velocity, α is the angular acceleration, and t is the time.

2. θ = θ_{0} + ω_{0}t + ½αt^{2}, where θ is the final angular displacement, θ_{0} is the initial angular displacement, and t is the time.

3. ω^{2} = ω_{0}^{2} + 2α(θ - θ_{0}), where ω is the final angular velocity, ω_{0} is the initial angular velocity, α is the angular acceleration, θ is the final angular displacement, and θ_{0} is the initial angular displacement.

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