Rotating Spring Problem A helical spring is rotated about one of its ends around a vertical axis. Investigate the expansion of the spring with and without an additional mass attached to its free end.

Overview Experimental Setup Experimental Results Theory Comparison Experimental Approach and Details Experimental Results Statistics and Graphics Theory The Physics Behind Rotating Spring Comparison Matching of Theory and Results Conclusion

Experimental Setup Vertical Axis Helical Spring

Experimental Details Relevant Parameters m (mass of spring): 2.3 g M (additional mass): 1.0, 2.0, 5.0 g  (angular velocity) lo (original length): 2.6 cm k (force constant): 2.5 N/m

Experiment Spring without mass 5 10 15 20 25 30 35 40 45 48

Results: Without mass

Experiment II Spring with mass 5 10 15 20 25 30 35 40 45 48

Results: With mass of 1 g

Results: With mass of 2 g

Results: With mass of 5 g

Theory Concept w Net force of Spring = Centrifugal Force

Theory parameters Centrifugal Force: Force to the right: Δ ηi ηi+1 ηi-1 Centrifugal Force: Force to the right: Force to the left:

Theory Newton’s second law of motion in equilibrium: Continuum Limit:

Theory General Solution: Sinusoid formula

Fitting: 0 g

Fitting: 1 g

Fitting: 2 g

Fitting: 5 g

Conclusion Without mass Distribution of the spring is nonuniform Denser at further end of the spring

Conclusion With mass More uniform distribution of the spring

Conclusion The variation of the length of spring at the end increases as: