Chapter 17 Motion in a circle
17.1
17.2
17.3
17.4
Uniform circular motion- object rotating at a steady rate
Angular displacement- Angle an object in circular motion turns through
Angular Speed- Rate of change of angular displacement of an object in circular motion
Angular Frequency- Number complete cycles a second
Circular motion- direction constantly changing so is constantly accelerating
Velocity is tangent to circle
Acceleration acts towards centre of circle
Centripetal- towards centre of circle
Centripetal force
Spotting UCM
1) Acceleration perpendicular to velocity
2) When v isn't perpendicular it doesn't apply
Resultant force acting on an object moving in a circle at constant speed
Acts towards centre
No matter the number of forces if the resultant acts towards centre the object will have circular motion
Top of Hill
Roundabout
Banked Track
Top of hill support for s is directly upwards in opposite direction to weight
Centripetal force towards centre of curvature
When s=0 car loses contact with road so we can calculate max speed for hill by subbing in s=0
Centripetal force comes from friction
To avoid skidding friction between tyres and road must be less that limit of friction- as speed increases as does friction
If friction limit exceeded the car will skid outwards to increase the radius to balance the equation
Banking means the normal reaction contributes to the centripetal force (Nsinθ) so higher speeds can be reached with no skidding
Calculations
No friction- all of centripetal force from normal
1) Resolve horizontally and vertically
2) Substitute to eliminate reaction force
3) Rearrange to find variable required
Written
May include friction
Ideal velocity where friction doesn't act
As speed increases friction increases down the track (contributes to centripetal) and stops car sliding up slope
Friction limit reached and car slides up slope to increase radius until centripetal force equals horizontal components of normal and friction again
Speed decrease- friction works in opposite direction but same principle
Big dipper
Long swing
Big wheel
Feel heavier as centripetal force acts up so forces up> forces down
Feel lighter as centripetal force acts down
Use energy conservation (KE=PE) to eliminate speed
If from horizontal to vertical height fallen through will be the same a length of cable WATCH FOR THIS
Takes passengers round in vertical wheel - turns fast enough to stop passengers falling and slow enough so they don't get crushed
Resolve forces based on position on the wheel (side is different to top and bottom is different to side)
Green arrow= acceleration Red arrow= velocity