Transcript V - Uplift Education

Uniform Circular
Motion
October 5, 6 2015
Circular Motion
• A is towards the center.
• V is tangential to the motion
• Speed is constant, V changes
• A 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.
Check 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!
Check your understanding …
Circular Motion Equations
• Vt= 2πr/T
• ac = vt2/r
Where
Vt = tangental velocity
R = radius
T = period (time required to make one complete
circle)
Ac = centripetal acceleration
Circular Motion– We do
• 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?
Vt= 2πr/T = 2*π*6.67X106m / 5292 sec = 7920 m/s
Circular 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/s2
NOTICE! 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.
Centripetal 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/s2. If the length of the rope is
2.1 m, what is the girl’s tangential speed?
2.5 m/s
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?
0.81 m
c. Correct the following statement: The racing car rounds the
turn at a constant velocity of 145 km/h.
Constant speed not constant velocity