# To investigate the relationship between Angular Acceleration and Torque.

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Introduction

Practical_CircMotion Anthony Paterson

Circular Motion Practical – UB Physics Assessment 1

Aim: To investigate the relationship between Angular Acceleration and Torque.

Hypothesis: Angular Acceleration will be proportional to torque (α α τ) according to the equationτ = Iα

Independent Variable:τ , Torque :

Torque was changed by varying both F and r in the formula τ = Fr .

Force is varied by changing the hanging mass and therefore the force due to gravity.

The radius (r) is varied by using different drive radii (shown in the method diagram), ie. applying the force due to gravity to the different sized rims underneath the cylinder being accelerated.

Dependant Variable:α , Angular Acceleration :

A cylinder on a low friction axle is accelerated by the independent variable - torque.

The measurements taken are the velocity at the rim and the diameter of the cylinder (to find r).

Variables to be controlled:

-Radius of velocity measurement.

The radius from the centre of rotation to the rim which the ticker tape was attached to was a constant 0.124m. Velocity measurements derived from the ticker tape therefore exist at this radius, so it is used to calculate angular velocity α=v/r.

-Radius of torque application.

Middle

6.855

0.180

1.800

0.150

14.516

13

0.096

0.960

0.075

7.742

14

0.103

1.030

0.075

8.306

15

0.110

1.100

0.075

8.871

16

0.112

1.120

0.075

9.032

Tape 2 | drive radius = 0.0252m | |||||||

radius of v = 0.124 | ||||||||

Period | mass = 500g | Torque | angular velocity | mass=1000g | Torque | angular velocity | ||

0.1 s | d | v | τ = Fr | ϖ = v/r | d | v | τ = Fr | ϖ = v/r |

m | msˉ¹ | Nm | r = 0.062 | m | msˉ¹ | Nm | r = 0.062 | |

1 | 0.008 | 0.080 | 0.124 | 0.645 | 0.022 | 0.220 | 0.247 | 1.774 |

2 | 0.016 | 0.160 | 0.124 | 1.290 | 0.043 | 0.430 | 0.247 | 3.468 |

3 | 0.027 | 0.270 | 0.124 | 2.177 | 0.069 | 0.690 | 0.247 | 5.565 |

4 | 0.039 | 0.390 | 0.124 | 3.145 | 0.091 | 0.910 | 0.247 | 7.339 |

5 | 0.049 | 0.490 | 0.124 | 3.952 | 0.114 | 1.140 | 0.247 | 9.194 |

6 | 0.062 | 0.620 | 0.124 | 5.000 | 0.137 | 1.370 | 0.247 | 11.048 |

7 | 0.073 | 0.730 | 0.124 | 5.887 | 0.163 | 1.630 | 0.247 | 13.145 |

8 | 0.089 | 0.890 | 0.124 | 7.177 | 0.187 | 1.870 | 0.247 | 15.081 |

9 | 0.096 | 0.960 | 0.124 | 7.742 | 0.206 | 2.060 | 0.247 | 16.613 |

10 | 0.107 | 1.070 | 0.124 | 8.629 | 0.233 | 2.330 | 0.247 | 18.790 |

11 | 0.122 | 1.220 | 0.124 | 9.839 | ||||

12 | 0.131 | 1.310 | 0.124 | 10.565 | ||||

13 | 0.142 | 1.420 | 0.124 | 11.452 | ||||

14 | 0.154 | 1.540 | 0.124 | 12.419 | ||||

15 | 0.170 | 1.700 | 0.124 | 13.710 |

Tape 3 | drive radius = 0.0352m | |||||||

Conclusion

Conclusion:

The graph Angular Velocity vs. Time was used solely to acquire several angular acceleration values for the Angular Acceleration vs. Torque graph.

However it does show the comparison of the angular acceleration caused by different masses combined with different drive radii.

The Angular Acceleration vs. Torque graph shows the important relationship; torque multiplied by 0.1 ± 0.02 kgm² is equal to angular acceleration.

This constant must be equal to I, from the equation τ = Iα where Irepresents rotational inertia.

The graph is a straight line graph with a positive gradient, which means Angular Acceleration is directly proportional to Torque, as stated in the hypothesis.

Evaluation:

The investigation was well designed, although error analysis was a problem.

Further investigations could include research into:

-the accuracy of ticker timers

-the accuracy of the way the ticker tape wraps around the rim of the cylinder/drum,

-the fluctuations of the cylinder’s radius.

This would enable use of absolute error to calculate derived errors for derived values such as Angular Acceleration.

The results are erroneous compared with the theoretical value of I. This is an error which can be investigated either to find the source of the discrepancy or the systematic error that caused this large difference in results.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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