# Force in a circle

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A2 lesson, force in a circle
Describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle
Recall and use centripetal acceleration
a = v2/r
Apply the equation F = ma to uniform motion in a circle to derive F = mv 2/r

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It might be worth pointing out to students that action-reaction pairs are not the same as balanced forces – while the latter act on just one object, the former act on two separate but interacting objects.
Newton’s third law is sometimes written as: “For every action, there is an equal and opposite reaction.”
• ### Force in a circle

1. 1. Force in a circle
2. 2. The Bucket of water • How does he not get wet? • What would happen if the handle snaps? http://www.youtube.com/watch?v=EPWmGttDCNY&feature=related
3. 3. Lesson Objectives • Describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle • Express angular displacement in radians • Recall and use centripetal acceleration a = v2 /r • Apply the equation F = ma to uniform motion in a circle to derive F = mv 2 /r
4. 4. What are the forces? centripetal” means “centre seeking”. Centripetal is an adjective describing the force; it is not the name of a special type of force, such as tension, gravity, magnetic force etc - e.g. pulling the bucket in with the ropecentrifugal, or centre-fleeing e.g. the force of the bucket on my hand Planetary orbits (almost!) gravitation Electron orbits electrostatic force on electron Centrifuge contact force (reaction) at the walls Gramophone needle the walls of the groove in the record Car cornering friction between road and tyres Car cornering on banked track component of gravity Aircraft banking horizontal component of lift on the wings
5. 5. Newton's 3rd law…. Every force has an equal and opposite reaction, so the force produced from the air, pushes the balloon in the opposite direction
6. 6. A force cannot exist on its own – there is always a second force acting against it. This forms the basis of Newton’s third law of motion states, which states: What is Newton’s third law? These pairs of forces that act between two objects are sometimes called action–reaction pairs. If object A exerts a force on object B, then object B exerts an equal but opposite force on object A.
7. 7. Centrifugal and Centripetal Force •The centripetal force is directed inward, towards the axis of rotation •As you swing the ball with the string, you feel the string tug on you hand...., this is called the centripetal force and is equal and opposite to the centrifugal force...
8. 8. the difference between linear and angular velocity • The instantaneous linear velocity at a point in the circle is usually given the letter v and measured in metres per second (m s-1 ). •The angular velocity is the angle through which the radius to this point on the circle turns in one second. This is usually given the letter w (Greek omega) and is measured in radians per second (rad s-1) http://www.animations.physics.unsw.edu.au/jw/circular.htm
9. 9. Deriving the formula for centripetal acceleration in terms of angular velocity Consider an object of mass m moving with constant angular velocity (w) and constant speed (v) in a circle of radius r with centre O. It moves from P to Q in a time t. The change in velocity Δv is parallel to PO and Δ v = v sinθ When θ becomes small (that is when Q is very close to P) sinθ is close to θ in radians. So Δ v = v θ To find the change in acceleration divide both sides by t a = Δ v / t = v θ / t Angular speeds w = θ / t, a = v w Since we also have v = w r (derived from last lesson), this can be written as a = v2 /r = v w = w2 r Applying Newton's Second Law (F = ma) gives: F = mv2 /r = m vw = m w2 r w = v / r
10. 10. The important formulas a= v2 / r F = Force (newtons) V = Velocity (m/s) r = Radius (m) m = Mass (kg) w = radial velocity rad s-1 F = m v w = m w2 r
11. 11. The turn table demo How long will these objects stay on? What forces are acting on these objects? Where is the best place to put the object to make it fly off the turntable 1. When a car turns a corner it can sometimes skid. Explain why, using the words velocity, friction, force
12. 12. Plenary - Answer This Question 1)You are sitting in the seat of a rollercoaster. Your mass is 50kg and the mass of the rollercoaster is 1000kg. You are travelling at a speed of 20 m/s. The centripetal force acting on you is 1000N. What is the radius of the ‘loop the loop’ you are travelling around? Draw a diagram of the rollercoaster and label the forces acting on it.