Circular Motion

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"if you want a holiday, take 2 weeks at the end of the term, then another 2 weeks at the end of the term, and eventually, you'll get a really long holiday called unemployment"

- Dr Ormande Waters

NO ANGULAR MOMENTUM LESGOOOOOOO

"hey chief! your villagers need you"

- Dr Ormande Waters

First practical: STAW Experiment 4.1: Going around in Circles

• Not marked
• BUT TAKE IT SERIOUSLY
• VERY IMPORTANT

Some SIS stuff

Accuracy: how close your results are to the “true” value. Relies on scale/error bar Precision: Fineness of equipment, how close your results are to each other Reliability: If you do more trials and results are basically the same Validity: does independent variable directly affect dependent variable, are there any other variables, known or unknown, that are impacting the results

"we'll make a start on the topic"

- Dr Ormande Waters

Horizontal Circular Motion

• Newton’s First Law: Any object in constant/uniform motion (speed/direction is not changing, thus velocity is not changing) will continue in that motion unless acted upon by an external/unbalanced force, and will continue to do this forever.
• Horizontal circular motion requires an unbalanced for acting
• Thus, for a projectile, the real force is gravity
• Centripetal Force: any force that causes an object to move continuously in a circle
  • Often a net force
  • “Centre” + “Seeking”
  • Has to be supplied by some other real force
  • Not a real force on its own
  • Towards the centre of circular motion
• No such thing as a centrifugal force

Real Forces

• Gravity
• Friction
  • Sideways friction, e.g. between car tyres and road
• Tension (tethered object)
  • Away from the object that is tethered towards the centre of circular motion
• Normal force
  • The action the car door furthest from turning circle on passenger
• Electric/Magnetic

Formula

$v=\frac{C}{T}=\frac{2\pi r}{T}=2\pi rf$

• T is period
• f is frequency

$a_c=\frac{v^2}{r}=\frac{4{\pi }^{2}r}{T^2}$

many contexts about direction, not always compass directions

Banked Corners

why are you late? (student answers) don't care! don't be late! - Dr Ormande Waters

$F_c=F_n\sin \theta =\frac{m{v}^2}{r}$ $F_n\cos \theta =mg$ $\tan \theta =\frac{v^2}{rg}$

Vertical Circular Motion

• Not necessarily uniform speed
• Also used for speed bumps
• At the top of the circle, tension is the least

$F_T=F_c-F_g=\frac{m{v}^2}{r}-mg$

• At the bottom, tension force is max
• At the sides:

$F_t=F_c+F_g=\frac{m{v}^2}{r}+mg$

this is going to be hot. oo oo aa aa oo oo aa aa - Dr Ormande Waters