Circular Motion

Rotation & Revolution Rotation Revolution Object rotating about an internal axis Ex. Daily motion of the Earth, spiral football Revolution Object rotating about an external axis Ex. Yearly motion of the earth around Sun

Circles, remember those! The distance AROUND a circle is the circumference C=2πr A tangent line is the line perpendicular to the radius at any point on the circle. TANGENT

2 ways to describe rotational motion Linear speed (Tangential Speed) Length of the path covered divided by time. Rotational speed Expresses how quickly you pass the same point on a circle. tire speed on car is measured in rotations-per- minute or RPM’s The Earth’s rotation is 24 hours in one day

Below, a record spinning on a axis through its center (black dot) Faster linear speed, Star or Smiley?? Smiley, travels a greater linear distance for the same time. Faster rotational speed, Star or smiley?? Both the same, they go 360 degrees in the same amount of time.

Are all people on Earth moving at the same speed?? Hmm.. Earth rotates from West to East Are some of us moving with a greater LINEAR SPEED than others??

Are all people on Earth moving at the same speed?? Are some of us moving with a greater LINEAR SPEED than others?? Yes, closer to the Equator, the faster you are moving…. Closer to poles, the slower you are moving Are some of us moving with a greater ROTATIONAL SPEED than others?? No, all people on earth have same rotational speed, because Earth is spinning at the same rate everywhere

What keeps us moving around with the earth so we don’t fly off? What direction does gravity pull? What keeps this stopper moving in a circle? What direction does the string pull? What keeps the roller coaster going around the loop? What direction does the track push?

Centripetal Acceleration Acceleration is any change in motion Changing direction (even at a constant speed) is acceleration. Your motion is changing in the direction of the center of the circle.

Centripetal Acceleration is the acceleration that causes an object to move in a circular path. ac = v2 v= linear speed r = radius of the curve r

Centripetal Acceleration What is the ac of a race car as it goes around a curve of radius 10 m at a velocity of 15 m/s? What is the direction of Acceleration? ac = v2 / r = (15)2 / 10 = 22.5 m/s2 Acceleration is always towards the center of the curve

The Rotor People Stand with backs against wall of a large cylinder, cylinder then starts spinning, and people are seemingly pushed against the wall, then floor drops, and people are stuck against the wall.

So why do you feel a force pushing you outward? A force does not cause this…… your INERTIA does!! Inertia is the tendancy for mass to resist changes to motion. Inertia makes you want to go flying in a straight line, and by going in a circle, you are going in a new direction all the time… Giving you the feeling of being pressed against the wall. The only actual force acting on you is the Centripetal Force, from the wall, pushing you towards the center

Centripetal Force Centripetal means “center- Seeking” Pulls you toward the center of the circle, keeps you moving in a circle Your inertia wants to go in a straight line The rails keep the cars on the track

Factors that affect centripetal Force Mass (m) – something with a larger mass requires more force to keep moving in a circle linear speed (vt) – something moving really fast requires more force to keep it in a circle, radius (r) – something moving in a circle of a small radius requires MORE force to keep it in a circle than it would with a large radius

A FAKE FORCE?? Centrifugal Force, like centrifuge, Inertia wants to take objects in a tangent line, perpendicular to the force pulling you into a circle This outward pushing is sometimes called the Centrifugal Force, like centrifuge, but it is not actually a force, it is only inertia

Centripetal Force Something more massive needs more force to keep it in a circle! Calculate the cent. force the tires need to overcome in order to keep the race car from going off the track where r = 10m, v = 15 m/s and the mass = 2000 kg. First find the centripetal acceleration ac = v2 /r = (15)2 / 10 = 22.5 m/s2 Then find the Force F=ma = 2000*22.5= 45000 N

Centripetal Force Where do you experience centripetal force? - the frictional force of the rubber tires of a car on a curved road, if there was no friction, your car would drive off the curve in a straight line… -gravitational force of the earth pulling the moon into orbit, if gravity was not there to provide the centripetal force, the moon would have no reason to move in a circle, it would go off into space in a straight line

Banked Curves and Tire Friction Most roads on highways and overpasses are actually tilted slightly upwards, or “banked” Why? During times of heavy rain or ice (low friction) the bank provides extra centripetal force to help the tires stay on the road while going around a curve