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.

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Presentation transcript:

Uniform Circular Motion October 5,

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 V t = 2πr/T a c = v t 2 /r Where V t = tangental velocity R = radius T = period (time required to make one complete circle) A c = centripetal acceleration

Circular 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? V t = 2πr/T = 2*π*6.67X10 6 m / 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 v t, then find a c. V t = 2πr/T = 2π*70m/60sec = 7.32m/s a c = v t 2 /r = (7.32 m/s) 2 / 70 m = 0.8 m/s 2 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/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/s 2. 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/s 0.81 m Constant speed not constant velocity