A kid excitedly swings his foam cut-out hammer. If point P acts like a pin and the hammer rotates about and a kg that point, what is the moment of inertia of the hammer? The foam has a density of p = 150 uniform thickness of t = 0.5 cm. Assume each cut-out is a rectangular plate and the foam acts as a rigid body. Plate A has a length 14 = 34 cm and width WA = 8 cm. Plate B has a length 1B = 8.5 cm and width wg = 30 cm. Plate C is identical to plate D, and has a length lc = 15 cm and width wo Plate C and D are attached to plate B such that their centers line up. Ip = 0.00758 x (kg) - m² 5 cm.

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**Title: Moment of Inertia of a Foam Cut-Out Hammer**

**Description:**

A kid excitedly swings his foam cut-out hammer. If point P acts like a pin and the hammer rotates about that point, what is the moment of inertia of the hammer? The foam has a density of \(\rho = 150 \ \frac{kg}{m^3}\) and a uniform thickness of \(t = 0.5 \ cm\). Assume each cut-out is a rectangular plate, and the foam acts as a rigid body.

### Diagram Explanation:

The diagram illustrates a foam hammer comprised of various rectangular plates labeled as A, B, C, and D. The hammer is held by a hand, with point P indicating the pivot point about which the hammer rotates. 

- **Plate A** acts as the handle of the hammer with dimensions:
  - Length \(l_A = 34 \ cm\)
  - Width \(w_A = 8 \ cm\)

- **Plate B** forms the central part of the hammerhead and has dimensions:
  - Length \(l_B = 8.5 \ cm\)
  - Width \(w_B = 30 \ cm\)

- **Plate C and Plate D** are identical and form the ends of the hammerhead, both having dimensions:
  - Length \(l_C = l_D = 15 \ cm\)
  - Width \(w_C = w_D = 5 \ cm\)

*Note: Plate C and D are attached to Plate B such that their centers line up.*

### Parameters:

- **Density of Foam (\(\rho\)):** \(150 \ \frac{kg}{m^3}\)
- **Thickness of Plates (\(t\)):** \(0.5 \ cm\)

### Task:

Determine the moment of inertia (\(I_P\)) of the hammer as it rotates about point P.

### Calculation:

\[
I_P = 0.00758 \ (kg \cdot m^2)
\]

---
*Content provided by UBC Engineering under a Creative Commons License.*
Transcribed Image Text:**Title: Moment of Inertia of a Foam Cut-Out Hammer** **Description:** A kid excitedly swings his foam cut-out hammer. If point P acts like a pin and the hammer rotates about that point, what is the moment of inertia of the hammer? The foam has a density of \(\rho = 150 \ \frac{kg}{m^3}\) and a uniform thickness of \(t = 0.5 \ cm\). Assume each cut-out is a rectangular plate, and the foam acts as a rigid body. ### Diagram Explanation: The diagram illustrates a foam hammer comprised of various rectangular plates labeled as A, B, C, and D. The hammer is held by a hand, with point P indicating the pivot point about which the hammer rotates. - **Plate A** acts as the handle of the hammer with dimensions: - Length \(l_A = 34 \ cm\) - Width \(w_A = 8 \ cm\) - **Plate B** forms the central part of the hammerhead and has dimensions: - Length \(l_B = 8.5 \ cm\) - Width \(w_B = 30 \ cm\) - **Plate C and Plate D** are identical and form the ends of the hammerhead, both having dimensions: - Length \(l_C = l_D = 15 \ cm\) - Width \(w_C = w_D = 5 \ cm\) *Note: Plate C and D are attached to Plate B such that their centers line up.* ### Parameters: - **Density of Foam (\(\rho\)):** \(150 \ \frac{kg}{m^3}\) - **Thickness of Plates (\(t\)):** \(0.5 \ cm\) ### Task: Determine the moment of inertia (\(I_P\)) of the hammer as it rotates about point P. ### Calculation: \[ I_P = 0.00758 \ (kg \cdot m^2) \] --- *Content provided by UBC Engineering under a Creative Commons License.*
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