Uniform circular motion What does the word uniform mean here constant radius and constant speed Velocity vector is tangent to the path at each instant so direction of velocity vector changes all the time as the object moves in circle ID: 816582
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Slide1
October 2014
Uniform Circular Motion
Slide2Uniform circular motion
What does the word “
uniform
” mean here? constant radius and constant speed
Velocity vector is tangent to the path at each instant, so direction of velocity vector changes all the time as the object moves in circle.
Therefore, there must be an inward-directed acceleration that causes the velocity to change its direction.
Slide3Circular Motion
is towards the center.is tangential to the motionSpeed is constant, changes force directed towards the center is what causes the acceleration (e.g. gravity,
a string)If the force is removed, the ball will continue in a straight line at the speed it had.
Slide4Check your understanding …
When a wheel rotates about a fixed axis, do all the points on the wheel have the same tangential speed?
Yes! Do they all have the same velocity? No!How do you know?
Slide5Check your understanding …
How do you know?
Slide6Circular Motion Equations
v
t= 2πr/Tac = vt2/rWhere
vt = tangental velocityR = radius T = period (time required to make one complete circle)ac = centripetal acceleration
Slide7Circular Motion– We do
The radius of a spacecraft orbiting earth is 6.67 x 10
6 m. If it orbits earth in 5292 seconds, what is the velocity of the spacecraft?vt= 2πr/T = 2*π*6.67X106m / 5292 sec = 7920 m/s
Slide8Circular Motion– We do
Jimmie Johnson is driving his #48 Lowe’s NASCAR around a bend that has a radius of 70 meters. It takes him 30 seconds to travel the track. What was the centripetal acceleration of Jimmie John’s #48 Lowe’s NASCAR?
Strategy: find vt, then find ac.vt= 2πr/T = 2π*70m/60sec = 7.32m/s
ac = vt2/r = (7.32 m/s)2 / 70 m = 0.8 m/s2NOTICE! T is time to go around a full circle. Jimmie went ‘around a bend’ which is half a circle. Thus, we need to double his time to get T.
Slide9Centripetal Acceleration – You do
a. A girl sits on a tire that is attached to an overhanging tree limb by a rope. The girl’s father pushes her so that her centripetal acceleration is 3.0 m/s
2. If the length of the rope is 2.1 m, what is the girl’s tangential speed? b. A boy swings a yo-yo horizontally above his head so that the yo-yo has a centripetal acceleration of 1.5m/s2. If the yo-yo’s tangential speed is 1.1m/s, what is the length of the yo-yo? c. Correct the following statement: The racing car rounds the turn at a constant velocity of 145 km/h. 2.5 m/s0.81 m
Constant speed not constant velocity
Slide10Dynamics of uniform circular motion
Object undergoing uniform circular motion is accelerating with centripetal acceleration
ac
, so it has a force acting upon it:
which must be directed toward the center of the circle.
It is called centripetal force.
Slide11it is not separate force – it is simply one of our familiar forces acting in the role of causing circular motion
Many forces can force an object to move in circular path, therefore becoming centripetal force:
Moon around the Earth ……… gravity
object sitting on a rotating table
(strawberries sitting on a seat of a turning car)
(a car moving in a circular path) ………… frictiona ball whirling in a circle at the end of a string ……… tension in the stringa person pressed against the inner wall of a rapidly rotating circular room in an amusement park …………. normal force from the wall Ferris–wheel rider passes through the lowest point of the ride ……. normal force from the seat and the force of gravity
Slide12useful relations
: - speed(linear) and angular speed
constant speed
period T: time required for one complete revolution (s)
speed v = distance/time
angular speed ω = angle swept/time Centrifugal (center-fleeing) Force - MISCONCEPTION
Slide13Circular Motion -
The radius of a spacecraft orbiting earth is 6.67 x 106 m. If it orbits earth in 5292 seconds, what is the velocity of the spacecraft?7919 m/s Jimmie Johnson is driving his #48 Lowe’s NASCAR around a bend that has a radius of 70 meters. It takes him 30 seconds to travel the track. What was the centripetal acceleration of Jimmie John’s #48 Lowe’s NASCAR? 3.07 m/s2
When a wheel rotates about a fixed axis, do all the points on the wheel have the same tangential speed?Yes Do they all have the same velocity? No
Slide14A 1000 kg car is going around a curve with radius 30 meters. If the coefficient of friction between the car's tires and the road is 0.5, what is the maximum speed at which the car can make the turn?
m = 1000 kg
r = 30 m
g = 9.8 m/s2maximum speed in the turn, v = ?v = 12 m/s