Circular Motion - Velocity<br />v<br />a<br />This involves any objects travelling in a circular path whether horizontal or vertical.<br />Velocity is at a tangent (90° to the radius) to the circular path.<br />Velocity equals the circumference divided by the time taken to ‘go around’ the circle i.e. 𝑣=𝑑𝑡 , 𝑑=2𝜋𝑟<br />So, 𝒗=𝟐𝝅𝒓𝑻<br />where T is called the ‘time period’ and is <br />the number of seconds for one orbit.<br /> <br />
Why is it accelerating? Why is there a centripetal force?<br /><ul><li>An object moving in a circle is accelerating. Accelerating objects are objects which are changing their velocity - either the speed (i.e., magnitude of the velocity vector) or the direction. An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction.
Without such an inward force, an object would continue in a straight line, never deviating from its direction. Yet, with the inward net force directed perpendicular to the velocity vector, the object is always changing its direction and undergoing an inward acceleration.</li></li></ul><li>Circular Motion - Acceleration<br />Acceleration is radially inwards (towards the center) and 𝒂𝒄=𝒗𝟐𝒓<br />The force is in the direction of the acceleration and as always is F=ma so since 𝑎𝑐=𝑣2𝑟<br />𝑭𝒄=𝒎𝒗𝟐𝒓<br /> <br />v<br />a<br />F<br />𝑭𝒄is the “centripetal force”<br /> <br />
http://www.youtube.com/watch?v=-G7tjiMNVlc<br />http://www.youtube.com/watch?v=L6-kn2tB-9E<br />Discuss with your neighbour what is supplying the centripetal force in the situations on the right….<br />
If the force an object in circular motion experiences is inward, why do we slide ‘outwards’ when driving around a sharp corner?HINT: SAME AS WHY DO WE LURCH FORWARD WITH A SUDDEN BRAKE?http://www.physicsclassroom.com/Class/circles/u6l1c.cfm<br />
Circular Motion is not always Horizontal…<br /><ul><li>When circular motion has vertical components we need to use vectors.
The sum of the unbalanced forces acting on the object give the resultant, centripetal force (Fc).
(Remember support force is perpendicular to the surface, weight force is always vertical) ….. Add vectors head to tail.
Add them together and we get…</li></ul>Support Force<br />W=mg<br />We will usually be given this angle… why?<br />𝜃<br /> <br />Fc<br />