Rotation

# Rotation - Mechanics and Modern Physics Dr. Bernd Stelzer...

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Dr. Bernd Stelzer Mechanics and Modern Physics PHYS 120 SFU Fall 2010 Dr. Bernd Stelzer

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Midterm 1 and MP2 October 19, 2010 Bernd Stelzer PHYS120 2 Mastering Physics (MP2) assignment is due today 9PM Midterm 1 takes place October 15 (during lecture) Cover chapters 1-7 of the book (excluding circular motion) 3 Questions (2 numeric and one set of multiple choice) Practice Midterm / answers posted on WebCT You should bring: Your Student ID Prepared formula sheet (download from WebCT) A ballpoint pen (pencil optional) Class calculator Aurex SC-6145 (or equivalent) Watch ( no cell phones allowed !) Arrive 5 min earlier, so we can start in time Drop bags / jackets in front of lecture hall
Uniform Circular Motion October 19, 2010 Bernd Stelzer PHYS120 3 v = 1 circumference 1 period = 2 π⋅ r T v t (t) = ds(t) dt ω = d θ dt = s(t) r Angular position = r ⋅θ Arc length Cartesian coordinates : x(t), y(t) are not the best choice to describe circular motion. For uniform circular motion: Position : r = const Speed : v = const = r d dt = r Angular position is measured counter clockwise

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Uniform Circular Motion – Graphical Representatio n October 19, 2010 θ f = i + ω⋅Δ t PHYS120 4 Bernd Stelzer
Centripetal Acceleration October 19, 2010 Bernd Stelzer PHYS120 5 a a a

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Centripetal Acceleration October 19, 2010 Since the direction of the linear velocity changes with time for an object undergoing circular motion, the object has to experience an acceleration . The motion diagram shows that this acceleration points towards the center of the circular path and it’s magnitude (not direction) is The radial acceleration of uniform circular motion is called “centripetal acceleration” a r = v 2 r = r ω 2 Centripetal = “center seeking” (Greek) PHYS120 6 Bernd Stelzer
Centripetal Acceleration October 19, 2010 Bernd Stelzer PHYS120 7 a r = v 2 r = r ω 2 Therefore:

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Question: October 19, 2010 Q: A ball on a string is swung in a horizontal circle. The string happens to break suddenly. Which trajectory does the ball follow? e PHYS120 8 Bernd Stelzer
Question: October 19, 2010 Q: A ball on a string is swung in a horizontal circle. The string happens to break suddenly. Which trajectory does the ball follow? e PHYS120 9 Bernd Stelzer

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Non Uniform Circular Motion October 19, 2010 Is this the only acceleration? Suppose an object’s rotation speeds up or slows down. We distinguish the radial (centripetal) and tangential acceleration. The later causes angular acceleration of an object. a t = dv t dt = r d ω dt = r α ⇒α = d dt The units of angular acceleration are rad/s 2 v t Note: Ћ is positive if Т is increasing counter clockwise and negative if is increasing clockwise PHYS120 10 Bernd Stelzer
Non Uniform Circular Motion October 19, 2010 Analogy with linear motion PHYS120 11 Bernd Stelzer

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