Walking on a merry-go-round

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October 4th 2009, 04:20 AM
m_i_k_o

Walking on a merry-go-round

Suppose that you are walking outwards along a radial line on a merry-go-round platform. You walk at a constant speed of 1 m/s. The platform is rotating at the rate of 20 RPM (RPM=Revolutions Per Minute).
What is the magnitude of your acceleration (in m/s2) when you are R meters away from the centre?

R[m] = 3.54;

Someone help me please
October 4th 2009, 05:25 AM
skeeter

Quote:

Originally Posted by m_i_k_o

Suppose that you are walking outwards along a radial line on a merry-go-round platform. You walk at a constant speed of 1 m/s. The platform is rotating at the rate of 20 RPM (RPM=Revolutions Per Minute).
What is the magnitude of your acceleration (in m/s2) when you are R meters away from the centre?

R[m] = 3.54;

Someone help me please

the acceleration is centripetal.
October 4th 2009, 10:50 PM
CaptainBlack

Quote:

Originally Posted by m_i_k_o

Suppose that you are walking outwards along a radial line on a merry-go-round platform. You walk at a constant speed of 1 m/s. The platform is rotating at the rate of 20 RPM (RPM=Revolutions Per Minute).
What is the magnitude of your acceleration (in m/s2) when you are R meters away from the centre?

R[m] = 3.54;

Someone help me please

Write the (vector) velocity equation out as a function of time and differentiate it to give the (vector) acceleration as a function of time, then as you are at a radius R at time t=R find the required acceleration and take its absolute value.

CB
October 7th 2009, 02:14 AM
Xapphire13

1 Attachment(s)

Quote:

Originally Posted by CaptainBlack

Write the (vector) velocity equation out as a function of time and differentiate it to give the (vector) acceleration as a function of time, then as you are at a radius R at time t=R find the required acceleration and take its absolute value.

CB

Like this? (Attached pic)
October 8th 2009, 12:00 AM
CaptainBlack

Quote:

Originally Posted by Xapphire13

Like this? (Attached pic)

Assume that $\theta=0$ at $t=0$

Then at time $t$ $(=R$ ) we have the velocity is:

$\bold{v}=[R \omega \sin(\omega t)+\cos(\omega t), R \omega \cos(\omega t)]+\sin(\omega t)] =$ $[t \omega \sin(\omega t)+\cos(\omega t), t \omega \cos(\omega t)]+\sin(\omega t)]$

So:

$<br /> \dot{\bold{v}}=[t \omega^2 \cos(\omega t), 2 \omega \cos(\omega t)+t \omega^2 \sin(\omega t)]<br />$

Now $\omega=\frac{2 \pi}{3}$ radians/s, so when $t=3.54$ we have:

$\dot{\bold{v}}\approx[6.61158,\ 15.8338]$ ,

so the magnitude of the acceleration is $\approx 17.16$ m/s^2

.. check the algebra and the arithmetic

CB