Centripetal Acceleration Physics

Turning: Turning counts as a form of acceleration because the direction of the velocity vector changes. Turning requires a force that is perpendicular to the current motion of an object.

Examples: Tetherball Cars using friction Image from: www.basketballhoopsunlimited.com

Blinky Car Demo Current Velocity Force If I push from behind the blinky car will speed up. If I push from the front the blinky car will slow down. But how do I make it turn? With a perpendicular force. (Tie or put the string perpendicular to the motion of the car so that it goes around the ring stand to show them how the blinky car turns). (I sent it our straight to them so that they could see the perpendicular position of the rope). Force

We can draw this on a circle: Force Current Velocity radial Centripetal Acceleration Tangent

CENTRIPETAL ACCELERATION CENTER or MIDDLE SEEKING or TOWARD Therefore Centripetal acceleration is: The acceleration of turning and it always points towards the center of the turn circle.

Tangential Velocity The velocity of an object right this second is always tangential to the track and perpendicular to the radius vector.

Which corner is the hardest to go around? Image from: mariokart.wikia.com Corners can be: Sharp Tight Sudden BUT scientists measure the radius of curvature to give it an number

Blinky Car Demo If we cut the string where will the car go? It will follow the tangential velocity in a straight line. Tie or put the sting around the ring stand. It forces the car the turn. Cut or let go of the string and the blinky car straightens out immediately.

Law of Inertia An object will NOT turn unless it is forced to. If the turning force is removed the object will straighten out IMMEDIATELY.

SLINGSHOT: Let’s say you are swinging slingshot in a circle trying to hit the bunny with a rock as shown by the picture below. Where should you let go of the rock to hit the bunny? BUNNY (First time people use a slingshot they release it at the wrong time completely. If you wait until the rock is between your eyes and the target the rock will go sideways). Have them discuss it with the people at their table and draw where they think it should go and why. Then ask for some comments. SIDEWAYS SIDEWAYS BEHIND

SLINGSHOT: Let’s say you are swinging slingshot in a circle trying to hit the bunny with a rock as shown by the picture below. Some people think you should let go here because it takes a curved path This is the actual path the rock would take. BUNNY SIDEWAYS This is VERY BAD because the rock has no memory. Inertia is straight so the rock straightens out immediately SIDEWAYS BEHIND

SLINGSHOT: Let’s say you are swinging slingshot in a circle trying to hit the bunny with a rock as shown by the picture below. Some people think you should let go when the slingshot is lined up with the bunny BUNNY SIDEWAYS This is BAD because remember the tangential velocity? The rock will follow the path of the tangential velocity. SIDEWAYS BEHIND

SLINGSHOT: Let’s say you are swinging slingshot in a circle trying to hit the bunny with a rock as shown by the picture below. You should let go of it about right here. BUNNY SIDEWAYS This is GOOD because the rock will follow the path of the tangential velocity. and hit the bunny. SIDEWAYS BEHIND

Let’s Review: https://www.youtube.com/watch?v=KvCezk9DJf k

In Class Demo: We are going to determine which circles require the most acceleration. We will use a bolt tied to a string, a drinking straw, and a Newton meter. When we spin the bolt it pulls on the string. The Newton meter shows me how hard it pulls.

How Hard We had to Pull: Big Slow Circle: Big Fast Circle: Small Slow Circle: Small Fast Circle:

Observations: The faster we spun the bolt the _____________ we had to pull. The bigger the circle was the ______________ we had to pull. harder less

Velocity: F = k v The turning force is DIRECTLY proportional to the velocity of the object. So if we spin faster the bolt accelerates more.

Radius of Curvature: F = k r Force is INVERSELY proportional to the turn radius.

EQUATION: ac = v2 r Put it all together Replace F with ac K = 1 Where And we get: Where ac = centripetal acceleration v = velocity r = radius ac = v2 r

Practice: ac = v2 r = (27)2 23 = 31.7 m/s2 = 3.23 g’s A car is driving 27 m/s around a corner with radius 23 meters. How much centripetal acceleration is required to make the car turn? Where does this acceleration come from? Have them work on this then check their answers. ac = v2 r = (27)2 23 = 31.7 m/s2 = 3.23 g’s (As much as a roller coaster at Lagoon) The acceleration comes from FRICTION between the tires and the road pushing the tire into the turn instead of letting it slide straight forward.

AIRPLANE LAB