# Rotational kinematics?

• djsharpsound

#### djsharpsound

hello, i am new to this board. i was having some problems with this problem?

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

Welcome,

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?

for any help

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:

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.

## 1. What is rotational kinematics?

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.

## 2. How is rotational kinematics different from linear kinematics?

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.

## 3. What is angular 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.

## 4. How is rotational kinematics used in real-world applications?

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.

## 5. What are the three equations of rotational kinematics?

The three main equations of rotational kinematics are:
1. ω = ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.
2. θ = θ0 + ω0t + ½αt2, where θ is the final angular displacement, θ0 is the initial angular displacement, and t is the time.
3. ω2 = ω02 + 2α(θ - θ0), where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, θ is the final angular displacement, and θ0 is the initial angular displacement.