# Parachutist landing on a turntable

• Dec 22nd 2010, 08:19 AM
FGT12
Parachutist landing on a turntable
A turntable in the shape of a flat uniform disk has a radius of 2m and a total mass of 120kg. The turntable is rotating at 3rad/s about a verticla axis through its centre. Suddenly a 70kg parachutist lands on the outer edge.(model parachutist as a particle. Find the angular speed of the turntable after the parachutist lands.

My working so far:
$\displaystyle I_a \omega_a = I_a_b \omega_a_b$
$\displaystyle \frac{1}{2}\times120\times2^2\times3 = [(\frac{1}{2}\times120\times2^2\times3) + (70\times2^2)]\omega_a_b$
$\displaystyle \omega_a_b = \frac{720}{1000}$
$\displaystyle \omega_a_b = 0.72$

however my textbook says 1.38 rad/s???????
• Dec 22nd 2010, 08:45 AM
emakarov
Quote:

A turntable in the shape of a flat uniform disk has a radius of 2m and a total mass of 120kg. The turntable is rotating at 3rad/s about a verticla axis through its centre. Suddenly a 70kg parachutist lands on the outer edge.
Happens all the time :)

Quote:

$\displaystyle \frac{1}{2}\times120\times2^2\times3 = [(\frac{1}{2}\times120\times2^2\mathbf{\times3}) + (70\times2^2)]\omega_a_b$
There should not be $\displaystyle \times3$ shown in bold above.
• Dec 22nd 2010, 12:08 PM
Ackbeet