Let's break down **Part C** into the requested two clear steps: --- ## **Step 1: Identify the initial and final linear momenta** From **Part A**, you found the initial linear momentum of the disk: \[ L_{\text{initial}} = 149~\text{slug} \cdot \text{ft/s} \] This was for a velocity \( v_{G1} = 7.83~\text{ft/s} \) in the positive x-direction. Now, the disk moves with a new velocity \( v_{G2} = -19.2~\text{ft/s} \) (the negative sign indicates the opposite direction). Since linear momentum is \( L = m v \), and the mass (m) remains the same: \[ L_{\text{final}} = m v_{G2} \] The ratio of the final and initial velocities will let us use the momentum from Part A: \[ L_{\text{final}} = 149 \times \frac{v_{G2}}{v_{G1}} = 149 \times \frac{-19.2}{7.83} = 149 \times (-2.453) = -365.5~\text{slug} \cdot \text{ft/s} \] **Explanation**: We calculated the new linear momentum using the mass (from Part A) and the new velocity (in the opposite direction). --- ## **Step 2: Calculate the change in linear momentum** Change in linear momentum (\( \Delta L \)) is: \[ \Delta L = L_{\text{final}} - L_{\text{initial}} = (-365.5) - (149) = -514.5~\text{slug} \cdot \text{ft/s} \] Since we want the magnitude (and usually report change as positive): \[ |\Delta L| = 514~\text{slug} \cdot \text{ft/s} \] (Rounded to three significant figures) **Explanation**: We subtracted the initial momentum from the final momentum to get the change. --- ## **Final Answer (Part C):** \[ \boxed{|\Delta L| = 514~\text{slug} \cdot \text{ft/s}} \] This is the change in the disk's linear momentum.

# Solution to Part C: Change in Linear Momentum ## **Step 1: Identify the Initial and Final Linear Momenta** ### Given Values - Initial momentum, \( L_{\text{initial}} = 149~\text{slug} \cdot \text{ft/s} \) - Final velocity, \( v_{G2} = -19.2~\text{ft/s} \) ### Calculation The final linear momentum can be calculated using the formula: \[ L_{\text{final}} = m \cdot v_{G2} \] Given that the mass (m) remains the same, we can express \( L_{\text{final}} \) in terms of initial momentum: \[ L_{\text{final}} = L_{\text{initial}} \cdot \frac{v_{G2}}{v_{G1}} \] Substituting the values: \[ L_{\text{final}} = 149 \cdot \frac{-19.2}{7.83} = 149 \cdot (-2.453) = -365.5~\text{slug} \cdot \text{ft/s} \] ### Explanation The final linear momentum was calculated by scaling the initial momentum with the ratio of the new velocity to the initial velocity. The negative sign indicates a change in direction. --- ## **Step 2: Calculate the Change in Linear Momentum** ### Formula The change in linear momentum can be calculated using: \[ \Delta L = L_{\text{final}} - L_{\text{initial}} \] ### Calculation Substituting the values: \[ \Delta L = -365.5 - 149 = -514.5~\text{slug} \cdot \text{ft/s} \] Taking the magnitude: \[ |\Delta L| = 514~\text{slug} \cdot \text{ft/s} \] ### Explanation The change in linear momentum was calculated by subtracting the initial momentum from the final momentum, resulting in a negative value that signifies the direction of change. The magnitude was taken for reporting. --- ## **Final Answer (Part C)** \[ \boxed{|\Delta L| = 514~\text{slug} \cdot \text{ft/s}} \]