1 Honors Physics 1 Class 11 Fall 2013 Propagation of Uncertainty Rotational quantities as vectors

2 Uncertainty in measurement Systematic or Random Random uncertainty arises from the fundamentals of a measurement or instrument. The measurement typically scatters about an average value. Brownian motion Counting statistics Thermal noise in electronics Quantum noise Systematic uncertainty is an error that you discover after the fact.

3 Determining uncertainty in a measured value

4 Reporting uncertainty

5 Propagation of Uncertainties in Deducing Unknowns How does the uncertainty in a particular measurement affect a calculated result? Brute force method: Plug the largest and smallest values of your measurement directly into the theoretical prediction and calculate the difference. Expansion approximation: Taylor expand your function about the measured point. Carefully add uncertainties together.

6 The Taylor Expansion

7 Taylor expansion for multiple variables

8 Adding uncertainties

9 Exercise A simple pendulum is used to measure g. The period of the pendulum is given by:

10 Rotational motion Definitions Vector directions

Definitions

Direction of Angular Displacement and Angular Velocity Use your right hand. Curl your fingers in the direction of the rotation. Out-stretched thumb points in the direction of the angular velocity.

Angular Acceleration

Equations for Constant 

Relationships Among Linear and Angular Variables

16 A test for conservative force

17 Honors Physics 2 - Persans S Curl math (3)