Collision With Linear and Angular Momentum

[drakoniis]

Homework Statement

Find the average force of the collision of a rolling complex object (assume sphere for inner object: 0.2m with another object along the edge with its density concentrated into a point: 1.2m from center, 10kg, and the total radius to contact surfaces is 1.2m) if the object is originally rolling without slipping, traveling at a velocity of 20 m/s, and is brought to a stop within 0.01m.

Homework Equations

v_0 = 20 m/s, \ \ \ v_f = 0 m/s
m_1 = 40 kg, \ \ \ r_1 = 0.2 m
m_2 = 10 kg, \ \ \ r_2 = 1.2 m
x_0 = 0 m, \ \ \ x_f = 0.01 m

The Attempt at a Solution

I'm trying using impulse, but I'm not sure how to include the rotational portion.

<br /> \begin{multline*}<br /> &amp; \overline{J} = \overline{F} \Delta t = M \Delta v \\<br /> &amp; \Delta t = \frac {\Delta x} {\overline{v}} = 1 * 10^{-2} s \\<br /> &amp; \overline F = \frac { M \Delta v } { \Delta t } = \frac {50 kg * 20 m/s} {1 * 10^{-2 }s} = 1 * 10^{-6} N<br /> \end{multline*}<br />

I also know the inertia, but I'm not sure how (and if) this factors into this equation.

 

[FedEx]

I am not able to understand the system of the two spheres.Are they concentric?

 

[drakoniis]

It's treated as a single sphere, but the fact there is another mass on the edge affects the inertia calculation.

 

[Feldoh]

I'll give you a hint the rotational inertia does matter.