Newton’s
2nd Law
Torque
& Inertia
Sensor
Data
Error
Analysis
Conducted an experimental validation of Newton’s Second Law for rotational motion using a PASCO rotational
apparatus with photogate sensors.
Calculated theoretical and experimental moments of inertia for a disk and a ring, correlating torque,
angular acceleration, and frictional effects.
Theoretical formulas:
Idisk = ½ mR², Iring = ½ m(R₁² + R₂²)
Experimental relation:
Ic = mh((g / a) − 1) r²
Disk — % Error
7.5 %
Theory vs Experiment
Ring — % Error
4 %
High accuracy match
Measured Acceleration (disk)
0.0087 m/s²
Avg. linear accel.
| Item |
Theoretical Ic (kg·m²) |
Experimental Ic (kg·m²) |
Error (%) |
| Disk |
0.00909 |
0.00846 |
7.5 |
| Ring |
0.00512 |
0.00537 |
4.1 |
- Verified Newton’s 2nd Law for rotation by linking ΣM = Iα through measured sensor data.
- Demonstrated relationship between torque, angular acceleration and moment of inertia.
- Quantified effect of friction and alignment errors on rotational measurements.
- Correlated experimental and theoretical models within < 8 % deviation.
Test setup and method
PASCO rotational apparatus with photogate/pulley system connected to data-acquisition software.
Measured angular velocity and linear acceleration for a 50 g suspended mass.
Derived moment of inertia experimentally from the relation Ic = mh((g/a) − 1)r² and
compared to theoretical values for disk and ring.
Author: Micah Haile | Instructor: Dave Carlgren | Southern Alberta Institute of Technology