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

[Enochfoul]

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

Attached as a photo

 

[drvrm]

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.

 

[Enochfoul]

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.

 

[drvrm]

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).

 

[drvrm]

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 !

 

[Enochfoul]

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?

 

[drvrm]

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.