Physics Teach Yourself Series Topic 2: Circular motion

Transcription

1 Physics Teach Yourself Series Topic : Circular motion A: Leel 14, 474 Flinders Street Melbourne VIC 3000 T: W: tssm.com.au E: info@tssm.com.au TSSM 013 Page 1 of 7

2 Contents What you need to know... 3 As it appears in Unit Circular motion... 3 As it appears in Unit Instantaneous elocity... 3 As it appears in Unit Acceleration... 6 The direction of the force... 6 Reiew Question... 6 The magnitude of the force... 6 Cars taking a horizontal cure... 6 Banked roads... 6 Reiew Question... 6 Leaning into cures... 6 Objects attached to strings... 6 Non uniform circular motion... 6 Solutions to Reiew Questions... 6 TSSM 013 Page of 7

3 As it appears in Unit 3 What you need to know Analyse the uniform circular motion of an object moing in a horizontal plane ( - a ehicle moing around a circular road; - a ehicle moing around a banked track; - an object on the end of a string; m R F net ) such as: Apply Newton s second law to circular motion in a ertical plane; consider forces at the highest and lowest positions only; Circular motion As it appears in Unit 3 For linear motion, if there is a non-zero resultant force then acceleration occurs in the direction of the net force resulting in a change in speed. Circular motion differs in that the elocity changes but the speed does not because the net force is acting at right angles to the direction of the motion. Instantaneous elocity As it appears in Unit 3 It is important to remember that there is a difference between speed and elocity. Velocity is a ector quantity haing both a magnitude and a direction while speed only has a magnitude. If an object traels in a circular path such as the one shown below the aerage elocity of the object will always be zero because it will always end up in the same place. Initial and final position Howeer, although the magnitude of the elocity will always be the same the direction will constantly be changing. TSSM 013 Page 3 of 7

4 The direction of the elocity is indicated by drawing a tangent to the circular pathway as shown below. So at any instant the elocity is tangential to the path and is at right angles to the radius and acceleration direction. The speed of an object can be calculated using the formula: d t Where: = speed (ms -1 ) d = distance (m) s = time (s) Howeer for objects traelling in a circular pathway it is more conenient to use the period (the time taken to complete a single reolution of a repeated circular motion) and circumference. So; circumference period The circumference of a circle = πr r T Where: r = the radius of the circle (m) T = period of the circle (s) TSSM 013 Page 4 of 7

5 Sample question A dog is attached to a 10 m long chain which is attached to a post in the ground so that the dog is able to run in circles around the post. It takes the dog 1 seconds to complete one circuit. Work out the following: i. What is the dog s aerage speed? r = 10m T = 1s 10 1 = 5. 4ms -1 ii. The dog completes 5 circuits, what is the dog s aerage elocity? If the dog completes 5 circuits then it is back in its original position so its aerage elocity is zero. iii. Assuming that the dog is traelling clockwise at a constant rate, determine its instantaneous elocity at point X. X When soling this kind of question it helps to indicate the direction of trael on the diagram. From the information supplied the dog had to be traelling due North at this point in time. The magnitude of the elocity was preiously established as being 5.4 ms -1 so the instantaneous elocity has to be 5.4 ms -1 north. TSSM 013 Page 5 of 7

6 Solutions to Reiew Questions 1. r T = 8 ms -1 T = 196 s r r m. The magnitude of the elocity is always the same so it must be 8 ms ms The diagram would look like this: Δ 5. a 4 r T r = 0.5 m T = 8.1 s a a ms towards the centre of the track. 6. F = ma m = 0.05kg a = 0.3 ms - F F N towards the centre of the track. TSSM 013 Page 6 of 7

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