Conservation of Linear and Angular Momentum
Objective:
Show that the linear and rotational momentum of the system is conserved during this rotational collision.
Set Up:
There are two set ups for this lab:
1) With a small downward ramp and a steel ball on top of a table, we will use the measurements of its final position to calculate velocity.
2)From there we have a rotating apparatus with a catch for the ball so we may use the found velocity to find the resulting rotation velocity.
Calculations:
We used what we know about the ball's moment of inertia and measurements of the ramp to the table to calculate the ball's theoretical velocity down the ramp without slip. From there we used the measurements of the ball's final location and solved the actual velocity of the ball which when compared to theoretical is smaller suggesting some slip. With this information we moved on to our second set up, but before doing so we have to calculate the inertia of the rotating apparatus in order to find the final momentum of the inelastic collision. To do so we used a hanging mass as a known source of torque then found the average value of alpha to determine the inertia of the apparatus. From there we placed the ball in a similar height on the ramp to have a consistent initial velocity and had it collide to the apparatus. With our calculations we found our final omega to be 1.87 rads/ s with a theoretical value of 2.43 rad/s.
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| Figure 1. Calculation for both set ups in the lab. |
It appears that since there is slip of the ball on the ramp greatly affects the value of the actual compared to the theoretical.
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