Circular Motion
Gravitron
Cars
Car Turning (has a curse) Rope Skip There must be a net inward force: Centripetal Force v2 F = maC a = C C R Centripetal acceleration 2πR v v v = R v T v 1 f = T
The motorcycle rider does 13 laps in 150 s. What is his period? Frequency?
R = 30 m [11.5 s, 0.087 Hz] What is his velocity?
[16.3 m/s] What is his aC?
[8.9 m/s2]
If the mass is 180 kg, what is his FC?
[1600 N]
The child rotates 5 times every 22 seconds...
What is the period?
60 kg [4.4 s] What is the velocity?
[2.86 m/s] What is the acceleration? Which way does it point?
[4.1 m/s2] What must be the force on the child?
[245 N]
Revolutions Per Minute (n)2πR v = 60 s
An Ipod's hard drive rotates at 4200 RPM. Its radius is 0.03 m. What is the velocity in m/s of its edge?
1 Airplane Turning
v = 232 m/s (520 mph)
aC = 7 g's
What is the turn radius?
[785 m = 2757 ft]
2 FC
Solving Circular Motion Problems
1. Determine FC (FBD) 2 2. Set FC = m v R 3. Solve for unknowns
The book's mass is 2 kg it is spun so that the tension is 45 N. What is the velocity of the book in m/s? In RPM?
R = 0.75 m
[4.11 m/s] [52 RPM]
What is the period (T) of the book?
[1.15 s] The car is traveling at 25 m/s and the turn's radius is 63 m. What must the μ be so it will not slip?
[1.01]
What must be the velocity of the ride if μ = 0.85?
R = 2.2 m
[5.04 m/s]
3 Other circles What is the velocity?
13o 0.85 m
2 kg
[0.66 m/s] What is the period?
[1.83 s] Banked turns (frictionless road) R = 220 m, v = 32 m/s. What must be the θ? N Ncosθ θ
Nsinθ
What is the turn radius of the plane (v = 53 m/s)?
10o
R = ?
4 Vertical Circles
If the car maintains a constant speed, what is the normal force at the top of the loop (m = 2.5 kg) ?
5 m
v = 14 m/s
[73.5 N]
What is the minimum speed needed for the car to make the loop without falling?
[7 m/s]
What is the maximum speed the car can go and not lose contact with the road at A? If it maintains that speed, what will be its normal force at B?
m = 750 kg R = 100 m
R = 100 m
[vA = 31.3 m/s] [NB = 14,700 N]
5 v2 v2 R 9.8 = 9.8 = 5 R v = 7 m/s
v2 9.8 = 10 v = 9.9 m/s
6 The skater feels 25% heavier at the bottom. What is his velocity (at the bottom)?
[3.13 m/s]
7