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# Physics a2 unit4_06_centripetal_force fb1 patrick (21-02-14) edited

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### Physics a2 unit4_06_centripetal_force fb1 patrick (21-02-14) edited

1. 1. 1. To consider speed & velocity around a circle 2. To consider acceleration as a change in velocity 3. To define an equation for acceleration when an object moves in a circular path 4. To define an equation for resultant force when an object moves in a circular path
2. 2. Velocity v n atio er cel ac If an object is moving in a circle with a constant linear speed, its velocity is constantly changing.... Because the direction is constantly changing.... If the velocity is constantly changing then by definition the object is accelerating If the object is accelerating, then an unbalanced force must exist
3. 3. Velocity vB B δθ C δv Velocity vB δθ Consider an object moving in circular motion with a speed v which moves from Velocity v point A to point B in δ t A seconds (From speed=distance / time), the distance moved along the arc AB, δ s is vδ t Velocity vA A The vector diagram shows the change in velocity δ v : (vB – vA)
4. 4. The triangles ABC & the vector diagram are similar Velocity vB B δθ C Velocity vA A Substituting for δs = vδt δv Velocity vB δθ If δθ is small, then δv / v = δs / r δv / v = vδt / r Velocity vA (a = change in velocity / time) a = δ v / δ t = v2 / r
5. 5. We can substitute for angular velocity.... a = v2 / r From the last lesson we saw that: v = rω a = (rω)2 / r (substituting for v into above) a = rω 2
6. 6. Velocity v n atio er cel ac We have seen already that any object travelling in a circular path is accelerating towards the centre of this circular path. This means that the resultant force is also pointing to the centre! (ΣF = ma)
7. 7. Velocity v But we know more…. We have learnt two things about the acceleration n atio er cel ac a = v2 / r (1) and a = rω 2 (2) YOUR TASK: Substitute the two equations (1) and (2) in Newton’s second law (ΣF = ma) and find the magnitude
8. 8. You should have found out that the magnitude of the resultant force is: Velocity v n atio er cel ac ΣF = mv2 / r or ΣF = mω 2r
9. 9. So, for any object of •mass m that travels at •linear speed v, moving in a circle of •Radius r, We know the following about the resultant force ΣF acting on it: •Direction: pointing towards the centre •Magnitude: ΣF = mv2 / r = mω 2r
10. 10. satellite Gravity Planet
11. 11. String ∑F = FT The point of support
12. 12. ∑F= F friction
13. 13. The wheel of the London Eye has a diameter of 130 m and takes 30 min for 1 revolution. Calculate: a. The linear speed of the capsule b. The linear acceleration c. The resultant force acting on a person with a mass of 65 kg
14. 14. The linear speed of the capsule : Using v = rω we know that we do a full revolution (2π rad) in 30mins (1800s) v = (130/2) x (2π / 1800) v = 0.23 ms-1
15. 15. The linear acceleration: Using a = v2 / r a = (0.23)2 / (130/2) a = 7.92 x 10-4 ms-2 The resultant force: Using ΣF = ma ΣF = 65 x 7.92 x 10-4 ΣF = 0.051 N
16. 16. An object of mass 0.150 kg moves around a circular path which has a radius of 0.420 m once every 5.00 s at a steady rate. Calculate: a. The speed and acceleration of the object b. The resultant force on the object [.528 ms-1, 0.663ms-2, 0.100N]