# Relative rotational motion on a disc

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In summary, the conversation discusses doubts and problems in determining the acceleration for a given problem involving rotational motion. The problem does not specify the frame of reference for the acceleration, causing confusion. The conversation also mentions difficulties in plugging data into the acceleration formula and a lack of understanding of relative rotational motion. The person in the conversation also points out an error in the equation and suggests using proper notation for cross products. Lastly, the importance of context and definitions for correctly interpreting equations is emphasized.
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Homework Statement
##A## oscillates along the central position ##O## with amplitude ##5 cm## at a frecuency ##2 hz## such that its displacement measured in ##cm## in function of time is governed by ##x=5sin(4 \pi t)##, where ##t## is measured in seconds. An angular acceleration around ##O## is applied to the disc with an amplitude ##20 rad## at a frequency ##4 hz## such that ##\theta =0.20sin(8 \pi t)##. Determine the acceleration of A for ##x=0 cm## and ##x= 5 cm##.
Relevant Equations
##\vec a=\vec a_B + \vec{\dot \omega} X \vec r + \vec \omega X \vec \omega X \vec r + 2. \vec \omega . \vec v_{rel} + \vec a_{rel}##
The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot \omega} X \vec r## would be ##x=5sin(4 \pi .5)## (in the second case), and then what numbers should I plug in ##\vec \omega X \vec \omega X \vec r##, ##2. \vec \omega . \vec v_{rel}## and ##\vec a_{rel}##?
I don't understand relative rotational motion very well. I mean, I just have to plug the data in the formula, but I don't know what's the data that I have.

Delta2
Like Tony Stark said:
Homework Statement: ##A## oscillates along the central position ##O## with amplitude ##5 cm## at a frecuency ##2 hz## such that its displacement measured in ##cm## in function of time is governed by ##x=5sin(4 \pi t)##, where ##t## is measured in seconds. An angular acceleration around ##O## is applied to the disc with an amplitude ##20 rad## at a frequency ##4 hz## such that ##\theta =0.20sin(8 \pi t)##. Determine the acceleration of A for ##x=0 cm## and ##x= 5 cm##.
Homework Equations: ##\vec a=\vec a_B + \vec{\dot \omega} X \vec r + \vec \omega X \vec \omega X \vec r + 2. \vec \omega . \vec v_{rel} + \vec a_{rel}##

The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot \omega} X \vec r## would be ##x=5sin(4 \pi .5)## (in the second case), and then what numbers should I plug in ##\vec \omega X \vec \omega X \vec r##, ##2. \vec \omega . \vec v_{rel}## and ##\vec a_{rel}##?
I don't understand relative rotational motion very well. I mean, I just have to plug the data in the formula, but I don't know what's the data that I have.View attachment 249344
There's something wrong with your equation. ##2. \vec \omega . \vec v_{rel}## would be a scalar.
For the cross products, use \times; and the triple cross product needs parentheses.

No equation is meaningful without a statement of the context and definitions of the variables. Please state these for your relevant equation.

## What is relative rotational motion on a disc?

Relative rotational motion on a disc refers to the movement of an object on a rotating disc in relation to another object or point on the disc. This motion can be described in terms of angular velocity, acceleration, and displacement.

## How is relative rotational motion different from absolute rotational motion?

Relative rotational motion takes into account the movement of an object in relation to another point on a rotating disc, whereas absolute rotational motion only considers the motion of the object in relation to a fixed point in space.

## What factors affect relative rotational motion on a disc?

The factors that affect relative rotational motion on a disc include the angular velocity of the disc, the distance from the center of the disc, and the mass of the object. The shape and size of the disc can also have an impact on the motion.

## How is relative rotational motion measured?

Relative rotational motion is typically measured using angular measurements, such as degrees or radians. The change in angular position over time, known as angular velocity, can also be used to measure relative rotational motion.

## What are some real-world applications of relative rotational motion on a disc?

Relative rotational motion on a disc has many practical applications. It is used in engineering for designing machines and mechanisms, in physics for understanding the motion of celestial bodies, and in sports for analyzing the movement of spinning objects like frisbees or discs in discus throwing events.

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