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Homework Help: Angular velocity question

  1. Mar 22, 2016 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations


    3. The attempt at a solution
    Attached as a photo

    Attached Files:

  2. jcsd
  3. Mar 22, 2016 #2
    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.
  4. Mar 22, 2016 #3
    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.
  5. Mar 22, 2016 #4
    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).
  6. Mar 22, 2016 #5
    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 !
  7. Mar 25, 2016 #6
    I have had another go and have attempted the second part.

    How do you think it looks now?

    Attached Files:

    • 1a.pdf
      File size:
      1.4 MB
    • 1b.pdf
      File size:
      1.5 MB
  8. Mar 26, 2016 #7
    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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