# Kinematics of Rotational Motion

• miamirulz29
In summary, the problem involves finding the magnitude of the angular velocity of a turntable after it has made one complete revolution, given the initial angular acceleration. Using the equation w^2 = w0^2 + 2αΔθ and simplifying, the solution is 2√(πα).
miamirulz29

## Homework Statement

A turntable that is initially at rest is set in
motion with a constant angular acceleration
α.
What is the magnitude of the angular ve-
locity of the turntable after it has made one
complete revolution?

## Homework Equations

w(omega)^2 = w(omegeInitial)^2 +2α(delta)θ

## The Attempt at a Solution

So then I used that because one revolution is equal to 2pi, I said w = sqrt. (4piα).
It is multiple choice and that is not one of the choices.
Here are the choices:
1. k~ωk = 2 π α
2. k~ωk = √2 π α
3. k~ωk = 2 α
4. k~ωk = 2√π α
5. k~ωk = √2 α
6. k~ωk = 4 π α
What am I doing wrong? Sorry if it is tough to read.

Not sure if you typed out the choices properly,but you can simplify you answer even more since √(ab) = (√a)*(√b)

Oh, I forgot to simplify, do it would be 2√π α

miamirulz29 said:
Oh, I forgot to simplify, do it would be 2√π α

if you mean 2√(πα), then yes

Yeah, that's what I meant. BTW, how do you type those symbols (I copy and pasted the symbols I could).

miamirulz29 said:
Yeah, that's what I meant. BTW, how do you type those symbols (I copy and pasted the symbols I could).

If you meant LaTex, in the reply box click on the [itex]\sum[/tex] symbol and you will get the list of symbols.

## 1. What is rotational motion?

Rotational motion is the movement of an object around a fixed point or axis. This type of motion is often seen in objects such as wheels, gears, and planets.

## 2. What is the difference between linear and rotational motion?

The main difference between linear and rotational motion is the type of path that the object takes. In linear motion, the object moves along a straight line, while in rotational motion, the object moves along a circular path around a fixed point.

## 3. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point or axis. It is calculated by dividing the change in angle by the change in time, and is typically measured in radians per second.

## 4. How is torque related to rotational motion?

Torque is a measure of the force that causes an object to rotate around an axis. It is directly proportional to the angular acceleration of the object and is affected by both the magnitude and direction of the applied force.

## 5. What is the moment of inertia in rotational motion?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is affected by both the mass and the distribution of mass in the object, and is often represented by the symbol "I" in equations.

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