Homework Help: Angular momentum (left or right movement)

1. Mar 30, 2012

careman

1. The problem statement, all variables and given/known data

A thin uniform rectangular sign hangs vertically above the
door of a shop. The sign is hinged to a stationary horizontal
rod along its top edge. The mass of the sign is 2.40 kg
and its vertical dimension is 50.0 cm. The sign is swinging
without friction, becoming a tempting target for children
armed with snowballs. The maximum angular displacement
of the sign is 25.0° on both sides of the vertical. At a
moment when the sign is vertical and moving to the left, a
snowball of mass 400 g, traveling horizontally with a velocity
of 160 cm/s to the right, strikes perpendicularly the
lower edge of the sign and sticks there.

Is the system (sign-snowball) going to move left or right?

2. Relevant equations

Conservation of angular momentum.

3. The attempt at a solution

Lost

2. Mar 30, 2012

Staff: Mentor

What's the angular momentum of the sign when it passes the vertical? Hint: Start by finding its moment of inertia.

3. Mar 31, 2012

careman

The moment of inertia is $I=\frac{1}{3}ML^2$, therefore the angular momentum of the sign when it passes the vertical is $L_s=Iω=(\frac{1}{3}ML^2)ω$.

4. Mar 31, 2012

Staff: Mentor

Excellent. Now find ω.

Once you've done that, figure out the initial angular momentum of the snowball.

5. Apr 1, 2012

careman

I found the angular velocity ω from the conservation of energy:

$\frac{1}{2}Iω^2=Mgh$
$ω=\sqrt{\frac{3g(1-cosθ)}{L}}=2.35 rad/s$

The angular momentum of the sign is $L_s=\frac{1}{3}ML^2=0.47 Nms$ while the angular momentum of the snowball is $L_b=mvL=0.32 Nms$

Comparing these two, the angular momentum of the sign is greater than the angular momentum of the ball, therefore the system is going to move to the left.

6. Apr 1, 2012

Good work!

7. Apr 1, 2012

careman

Thank you for your help and for checking my work. I really appreciate it.