Homework Help: Collision With Linear and Angular Momentum

1. Dec 1, 2007

drakoniis

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

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.

2. Relevant equations

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

3. The attempt at a solution

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

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

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

2. Dec 1, 2007

FedEx

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

3. Dec 1, 2007

drakoniis

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

4. Dec 1, 2007

Feldoh

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