Go Back   Physics Help Forum > High School and Pre-University Physics Help > Periodic and Circular Motion

Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Feb 23rd 2011, 12:11 AM   #1
Junior Member
 
Join Date: Aug 2009
Posts: 18
Difficult Merry-Go-Round Question?

A merry-go-round of radius 9.7m is rotating at 3.2 rpm. It slows uniformly to a stop in 17s. At the time it begins to slow down, Harry is sitting on a horse at the edge of the merry-go-round situated on the positive x axis.

a Write expressions for Harry's position, velocity and acceleration vectors (x and y components) as a function of time.

b Find Harry's displacement vector and his angular displacement for the time that the merry-go-round is slowing down.

I have no clue how to start this problem. Please help.
KaylaN is offline   Reply With Quote
Old Feb 23rd 2011, 06:42 AM   #2
Physics Team
 
Unknown008's Avatar
 
Join Date: Jun 2010
Location: Mauritius
Posts: 609
You know that this will involve the trigonometric functions cosine and sine?

Hint:
x is first maximum, then goes to zero, then to a minimum, then back to zero and the maximum.
y is first at zero, to a maximum, to zero again, then a minimum and back to zero.
__________________
Jerry (Got my results!)
It is easier to protect your feet with slippers than to cover the earth with carpet.
No one can go back and change a bad beginning; but anyone can start now and create a successful ending.

If a problem can be solved, no need to worry about it. If it cannot be solved what is the use of worrying?
Unknown008 is offline   Reply With Quote
Old Feb 23rd 2011, 08:53 AM   #3
Junior Member
 
Join Date: Aug 2009
Posts: 18
here is what I got so far.

The way this has to be done is to find the angle as a function of time: In particular,
θ'' = (d/dt)^2 (θ) = - α = - ω0/17

θ' = dθ/dt = ω0 - αt

θ = 0 + ω0*t - αt^2/2

Therefore:
θ(t) = ω0*t - αt^2/2

where
ω0 = (2π*3.2/60) = (π*32/300) = (π*8/75)
α = ω0/17 = 8π/(17*75)

Harry's displacement is:
(x,y) = 9.7*(cosθ, sinθ) = 9.7*(cos(ω0*t - αt^2/2), sin(ω0*t - αt^2/2))

Harry's velocity is:
(v_x, v_y ) = (d/dt)(x,y) = 9.7*(ω0 - αt)(-sin(ω0*t - αt^2/2), cos(ω0*t - αt^2/2))

Harry's acceleration is:
(a_x, a_y) = (d/dt)(v_x, v_y)
KaylaN is offline   Reply With Quote
Old Feb 23rd 2011, 10:50 AM   #4
Physics Team
 
Unknown008's Avatar
 
Join Date: Jun 2010
Location: Mauritius
Posts: 609
It seems right to me. Now the displacement and angular displacement should be easier.
__________________
Jerry (Got my results!)
It is easier to protect your feet with slippers than to cover the earth with carpet.
No one can go back and change a bad beginning; but anyone can start now and create a successful ending.

If a problem can be solved, no need to worry about it. If it cannot be solved what is the use of worrying?
Unknown008 is offline   Reply With Quote
Old Feb 23rd 2011, 11:12 AM   #5
Junior Member
 
Join Date: Aug 2009
Posts: 18
Where do you start to find the displacement vector and angular displacement? I have no clue.
KaylaN is offline   Reply With Quote
Old Feb 23rd 2011, 11:20 AM   #6
Physics Team
 
Unknown008's Avatar
 
Join Date: Jun 2010
Location: Mauritius
Posts: 609
On your sketch, the starting point is at 9.7 m on the x-axis. The last point is at the position (x, y) at t = 12s. Then, the distance between the starting point and the last point gives the magnitude of the displacement, and then, you have to find the angle (say between a vertical line to the last point). You will need to know some circular measure for that.

The angular displacement is simply given by:

θ(t) = ω0*t - αt^2/2

when t = 12 s
__________________
Jerry (Got my results!)
It is easier to protect your feet with slippers than to cover the earth with carpet.
No one can go back and change a bad beginning; but anyone can start now and create a successful ending.

If a problem can be solved, no need to worry about it. If it cannot be solved what is the use of worrying?
Unknown008 is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Periodic and Circular Motion

Tags
difficult, merrygoround, question



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Merry Christmas topsquark General Physics 2 Dec 26th 2015 07:41 AM
Difficult question with work asking for mass s3a Energy and Work 1 Jun 17th 2009 12:24 PM
Torque on merry-go-round Alexrey Advanced Mechanics 3 May 14th 2009 12:56 AM
Difficult question on Motion & Force(need guidance..tq) jonbrutal Kinematics and Dynamics 6 Feb 5th 2009 06:42 AM
round trip speed of light evabern Special and General Relativity 5 Jul 28th 2008 01:12 PM


Facebook Twitter Google+ RSS Feed