How Do You Calculate Angular Velocity and Force in Rotational Motion?

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Discussion Overview

The discussion revolves around calculating angular velocity and force in the context of rotational motion, specifically addressing a homework problem involving a mass attached to a string and rotating in a horizontal circle. Participants explore both theoretical and practical aspects of the problem, including the necessary formulas and diagrams for clarity.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents a problem involving a mass rotating in a horizontal circle and seeks advice on calculating angular velocity and the force on a table.
  • Another participant questions the validity of the initial solution, suggesting that the speed may be too large and recommends drawing diagrams to represent forces.
  • There is a discussion about the necessity of diagrams and whether limited information affects the calculation of angular velocity.
  • Participants emphasize the importance of defining angles and resolving forces, particularly the tension in the string and the weight of the mass.
  • One participant outlines the forces acting on the mass, including weight, normal reaction, and centripetal force, while noting the absence of friction in the discussion.
  • Clarification is sought regarding whether the mass is hanging or rotating on a table, which affects the analysis of forces involved.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the initial calculations and the need for diagrams. There is no consensus on the correct approach to the problem, and multiple viewpoints regarding the setup and calculations remain present.

Contextual Notes

Participants note limitations in the problem's information, such as the lack of details about friction and the specific setup of the mass's rotation. The discussion reflects various assumptions about the forces acting on the system and the definitions of angles involved.

Who May Find This Useful

This discussion may be useful for students and educators in physics or engineering who are exploring concepts related to rotational motion, angular velocity, and force analysis in practical scenarios.

Enochfoul
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Homework Statement



Hi Everyone would somebody please be able to give some advice on the following questions:
Part (a)
A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its angular velocity.

I have attached a solution does it look right or is there a more efficient way to calculate it?

Part (b)
If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg.

I'm a little bit stuck any idea what formula I would use to begin to solve it? Thanks in advance

Homework Equations



Fc=mω^2r

The Attempt at a Solution


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Enochfoul said:
I have attached a solution does it look right or is there a more efficient way to calculate it?

part A--pl. check your solution - as the speed is very large! you may draw a diagram to represent forces
in part b also draw a free body diagram.
 
drvrm said:
part A--pl. check your solution - as the speed is very large! you may draw a diagram to represent forces
in part b also draw a free body diagram.
Hi Thanks for the reply.

In relation to my solution there is limited info in the question. Would a diagram be necessary to solve the problem as I believe (but I am probably wrong) that I have calculated the relevant numbers to enter into the formula.

Is there a more efficient way of calculating Angular velocity? given that I only have two pieces of information. The length and the height.
 
Enochfoul said:
In relation to my solution there is limited info in the question. Would a diagram be necessary to solve the problem as I believe (but I am probably wrong) that I have calculated the relevant numbers to enter into the formula.

Is there a more efficient way of calculating Angular velocity? given that I only have two pieces of information. The length and the height.

In your answer you must define the angle carefully- for example you write cos of theta = h/L -so you are taking theta angle as the angle made by the string with the vertical drawn at point of suspension.
you have two forces working -
1. the tension in the string pulling along length-you are calling it F
2. the weight of the bob acting vertically down ward
for the motion in circular path to be sustained you need one centripetal force acting horizontally towards the centre , which must be provided by the unbalanced force available to the system .
therefore resolve the weight m.g in the direction along length opposite to the F and these two balance each other-must be equal.
the other resolved component along the horizontal radial direction of m.g will give you the centripetal force and calculate ang. velocity-see if it changes your answer- then we may tackle part (b).
 
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Enochfoul said:
Part (b)
If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg.

I'm a little bit stuck any idea what formula I would use to begin to solve it? Thanks in advance

you just liked my previous post but i will request to work it out so that a check can be done with numbers!
now coming to the part -b-

the ball is rotating on the table so figure out the forces -
1. ball's weight acting vertically downward.
2. the normal reaction perpendicular to table passing through the centre of the ball--...
3. as it is rotating the required centripetal force pointing towards the centre- must be provided by the string
you have not said anything about the friction -so one can not do more !
 
drvrm said:
you just liked my previous post but i will request to work it out so that a check can be done with numbers!
now coming to the part -b-

the ball is rotating on the table so figure out the forces -
1. ball's weight acting vertically downward.
2. the normal reaction perpendicular to table passing through the centre of the ball--...
3. as it is rotating the required centripetal force pointing towards the centre- must be provided by the string
you have not said anything about the friction -so one can not do more !
I have had another go and have attempted the second part.

How do you think it looks now?
 

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Enochfoul said:
I have had another go and have attempted the second part.

How do you think it looks now?

now part a seems to be good -numbers may be checked.
part b i have a question?
Is the ball hanging and rotating on a horizontal table ?
or the ball is rotating on the table about a centre 0 attached with the string?
If the case of first one the additional force is normal reaction of the table on the ball. so your work out seems to be good.
 

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