Average Linear Angular Torque Mass Tension Time Acceleration Acceleration a (rad/s?) Time m |(s) T (N) (m N) t (s) US ths a (m/s) (kg) |25.94 0.050 |(50 grams) 25.68 37.56 17.06 0.100 |(100 grams) 25.95 17.39 0.150 11.64 (150 grams) 13.05 16.345 www 10.94 T4.53 11.18 0.200 (200 grams) 9.36 9.64 14.29 .250 (250 grams)
Average Linear Angular Torque Mass Tension Time Acceleration Acceleration a (rad/s?) Time m |(s) T (N) (m N) t (s) US ths a (m/s) (kg) |25.94 0.050 |(50 grams) 25.68 37.56 17.06 0.100 |(100 grams) 25.95 17.39 0.150 11.64 (150 grams) 13.05 16.345 www 10.94 T4.53 11.18 0.200 (200 grams) 9.36 9.64 14.29 .250 (250 grams)
Average Linear Angular Torque Mass Tension Time Acceleration Acceleration a (rad/s?) Time m |(s) T (N) (m N) t (s) US ths a (m/s) (kg) |25.94 0.050 |(50 grams) 25.68 37.56 17.06 0.100 |(100 grams) 25.95 17.39 0.150 11.64 (150 grams) 13.05 16.345 www 10.94 T4.53 11.18 0.200 (200 grams) 9.36 9.64 14.29 .250 (250 grams)
All information is there plus formulas to compete calculations.
Please answer for the rest of the table by gram (linaer acceleration, angular acceleration, tension, torque) with given measurements and formulas.
Transcribed Image Text:### Moment of Inertia Calculations
#### Components and Calculations
1. **Shaft**
- Moment of Inertia Formula: \(\frac{1}{2}MR^2\)
- Calculated Moment of Inertia: \(0.00000167 \, \text{kg} \cdot \text{m}^2\)
2. **Threaded Rod**
- Moment of Inertia Formula: \(\frac{1}{2} MRd^2\)
- Calculated Moment of Inertia: \(0.00378012 \, \text{kg} \cdot \text{m}^2\)
3. **0.1-kg Masses**
- Total Moment of Inertia: \(2 \cdot (1\text{kg}) \cdot d^2\)
- Calculated Moment of Inertia: \(52.8125 \, \text{kg} \cdot \text{m}^2\)
4. **4 Wing Nuts**
- Moment of Inertia Formula: \(M \cdot \text{wingnuts} \cdot d^2\)
- Calculated Moment of Inertia: \(4.1790625 \, \text{kg} \cdot \text{m}^2\)
5. **Total Moment of Inertia**
- Sum of all components: \(56.9953594 \, \text{kg} \cdot \text{m}^2\)
#### Measurements and Masses
- **Height (h):**
- 0.7 m
- **Masses:**
- Mass of Shaft: \(0.3924 \, \text{kg}\)
- Mass of Threaded Rod: \(0.0628 \, \text{kg}\)
- Mass of 0.1-kg Mass: \(0.1 \, \text{kg}\)
- Mass of 4 Wing Nuts: \(0.0234 \, \text{kg}\)
#### Dimensions
- **Radius of Shaft:**
- \(0.00925 \, \text{m}\)
- **Length of Threaded Rod:**
- \(0.34 \, \text{m}\)
- **Distances \(d\) from Center:**
- \(0.1625
Transcribed Image Text:### Rotational Dynamics Experiment Data Analysis
**Equipment Contributions to Moment of Inertia:**
| Component | Moment of Inertia (kg·m²) |
|-------------------------------|---------------------------|
| Shaft | 0.00000128 |
| Threaded Rod | 0.00237802 |
| 0.1 kg Masses (2 masses) | 52.81235 |
| 4 Wing Nuts | 0.17906103 |
| **Total Moment of Inertia** | 55.99353033 |
**Distance Measurements:**
- Height (H): 0.720 m
- Radius (r): 0.07 m
**Experiment Data:**
| Mass \( m \) (kg) | Time (s) | Average Time \( t \) (s) | Linear Acceleration \( a \) (m/s²) | Angular Acceleration \( \alpha \) (rad/s²) | Tension \( T \) (N) | Torque \( \tau \) (m·N) |
|-------------------|--------------|--------------------------|-----------------------------------|---------------------------------------------|--------------------|--------------------------|
| 0.050 (50 grams) | 25.49, 25.87 | 25.75 | | | | |
| 0.100 (100 grams) | 17.06, 17.39 | 17.225 | | | | |
| 0.150 (150 grams) | 11.64, 13.65 | 12.645 | | | | |
| 0.200 (200 grams) | 16.94, 11.18 | 14.06 | | | | |
| 0.250 (250 grams) | 9.36, 9.86 | 9.61 | | | | |
**Formulas:**
- Linear Acceleration: \( a = \frac{2H}{t^2} \)
- Angular Acceleration: \( \alpha = \frac{a}{R} \)
- Tension Calculation: \( T = m(g - a) \) with \( g = 9.80 \, \text{m/s}^2 \)
- Torque
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
