Procedure

Experimental Procedure

1. Preparation and Setup

1. Place the rigid disc on a low‑friction horizontal axle so that it can rotate freely.
2. Wind a light, inextensible string around the disc's circumference.
3. Attach a known mass $m$ to the free end of the string.
4. Ensure that the string is aligned properly and does not overlap or slip during rotation.
5. Set up the measurement devices such as:
   • A timer or digital stopwatch
   • Angular velocity $\omega$ and angular displacement $\theta$ sensors (if available)
   • Scale to measure height and mass

2. Initial Measurements

1. Measure and record the mass of the disc, radius of the disc $r$, and moment of inertia $I$ if provided.
2. Measure the mass of the hanging object using a digital balance.
3. Mark and measure the height $h$ through which the mass will fall.
4. Ensure the disc and string are at the initial rest position before starting the experiment.

3. Performing the Trial

1. Hold the hanging mass at the predefined height such that the string is fully taut.
2. Confirm that there is no initial angular or linear motion.
3. Release the mass gently without applying any push, ensuring that motion begins only due to gravity.
4. As the mass descends, it will cause the disc to rotate.
5. Record the following during the motion:
   • Time taken for the mass to reach the bottom
   • Angular velocity $\omega$ readings at regular intervals (if sensors are available)
   • Total number of rotations completed by the disc

4. Post‑Motion Measurements

1. Once the mass reaches the bottom, immediately stop the timer.
2. Measure the final linear velocity $v$ using time–distance calculations (if required).
3. Record the final angular velocity $\omega$ from sensor readings or calculate it using the relationship $v = r\omega$.

5. Data Analysis

1. Compute the angular acceleration using: $\alpha = \frac{\Delta\omega}{\Delta t}$
2. Calculate tension $T$ in the string using: $mg - T = ma$
3. Calculate the torque $\tau$ acting on the disc: $\tau = rT$
4. Verify Newton's Second Law for Rotation by checking whether: $\tau \approx I\alpha$
5. Compute the following energies:
   • Translational kinetic energy: $KE_{\text{tran}} = \frac{1}{2}mv^{2}$
   • Rotational kinetic energy: $KE_{\text{rot}} = \frac{1}{2}I\omega^{2}$
6. Compute the initial gravitational potential energy: $PE = mgh$
7. Check the work–energy theorem: $mgh \approx KE_{\text{tran}} + KE_{\text{rot}}$

6. Interpretation and Conclusion

1. Compare the experimental values of torque and angular acceleration with the theoretical predictions.
2. Evaluate whether the relationship $\tau \approx I\alpha$ holds true within acceptable experimental error.
3. Examine the agreement between potential energy lost and total kinetic energy gained to verify the work‑energy theorem.
4. Identify and discuss possible sources of error such as:
   • Friction in the axle
   • Air resistance
   • Stretching of the string
   • Measurement inaccuracies

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Simulation Procedure

1. Set the initial conditions by selecting the disc radius, mass of disc, mass of hanging object, and height of fall.
2. Click the "Start" button to release the mass and begin the rotation.
3. Observe real‑time readings of:
   • Angular velocity $\omega$
   • Angular acceleration $\alpha$
   • Time elapsed
   • Work and energy values
4. Track the number of complete rotations using an automatic counter.
5. Use the in‑built measurement tools to extract necessary values.
6. Compute the torque using the given equation.
7. Verify the relation using recorded data.
8. Compare experimental work done with calculated rotational kinetic energy.
9. Analyze and interpret the results using the data visualization tools available in the virtual lab.

Simulation Outputs

• Torque vs. Angular Acceleration Graph (should be linear).
• Work Done vs. Energy Change (should be equal).
• Number of Rotations vs. Fall Height.

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Observation Table

Moment of Inertia $I$ (kg·m²)	Linear Velocity $v$ (m/s)	Angular Velocity $\omega$ (rad/s)	Angular Acceleration $\alpha$ (rad/s²)	Rotational Kinetic Energy (J)	Translational Kinetic Energy (J)	Total Kinetic Energy (J)	Initial Potential Energy (J)
1.
2.

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