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3.1-3.2 Circular Motion

3.1-3.2 Circular Motion. Let’s take a look at your diagram. During your investigation, you might have noticed a few things when you released the stopper at various points. Is velocity constant when an object moves in a circle?.

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3.1-3.2 Circular Motion

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  1. 3.1-3.2 Circular Motion

  2. Let’s take a look at your diagram • During your investigation, you might have noticed a few things when you released the stopper at various points

  3. Is velocity constant when an object moves in a circle? • Can you keep an object moving at a constant velocity when it moves in a circle? • THE ANSWER IS YES AND NO • What aspect of velocity can you keep constant? • What aspect of velocity changes?

  4. Direction changes, speed is constant • Even though only one aspect of the velocity vector changes, that still means change • And a change in velocity means… • ACCELERATION • And where there is acceleration, there is… • FORCE

  5. Constant speed, changing direction • Circular motion can be seen as a large number of straight velocity vectors adding up to give you circular motion • Much like a circle itself can be made up of a large number of small straight lines • The smaller those lines are, the closer you get to a perfect circle

  6. See the progression?

  7. What forces do you feel? • When you are spinning the mass, what forces did you feel? • What keeps the mass from flying out of the circle (which is what happens when you let go…)

  8. Centrifugal vs. Centripetal force • You will notice that when the mass spins, it pulls out of the circle • Think about what happens when you spin a small child around by their arms – what do you notice? • This force – the force that a spinning mass seems to exert outwards – is known as the CENTRIFUGAL FORCE

  9. What keeps the mass from flying away? • If the mass pulls outwards during circular motion, the one thing keeping it from flying out MUST be an opposing force inwards • In the case of your little experiment, what was it?

  10. Centripetal force • In the case of your experiment, the tension in the string provides what is known as a CENTRIPETAL FORCE that pulls inward • This constant force “yanks” the mass inwards, forcing the velocity vector to constantly turn inwards • Therefore, if the force pulls inwards – so does the acceleration it causes

  11. Centripetal force is external to the mass • This could be string, a rod – anything that is attached to the rotating mass that keeps it from flying out of its rotational circle • Even gravity – planets move around the sun at a constant speed in a circular motion because the sun’s gravitational pull creates a centripetal force that keeps us in orbit • If the planets did not maintain a constant speed, what would we notice on earth?

  12. Which one do we pay attention to? • Essentially, if an object is moving uniformly in a circle, it means that the centrifugal and centripetal forces are balanced out • Most questions will ask you to find centripetal force – and usually it is assumed if we are dealing with uniform motion that they are equal

  13. Centrifugal force is described via the the rotating mass • Centrifugal force is a necessary “invisible” force used to describe the path of objects moving in a circle • Since a rotating object is in a non-inertial frame of reference that means that the forces the mass experiences must be explained somehow • As you spun the mass faster, what did you notice? • The greater the speed of the object rotating, the larger the centrifugal force, therefore requiring a larger centripetal force to keep it in a circle

  14. A false force • Centrifugal force is a false force – it is the force “felt” by an object due to its inertia • The object wants to maintain its motion, so it resists the centripetal force being applied • This gives the impression of a “force” being produced that opposes the centripetal

  15. Centripetal acceleration pulls inwards – but don’t forget that the mass “pulls” outwards creating the sensation of centrifugal acceleration v1 Fcp Fcf v2

  16. At an instant in the object’s path – notice that the vector doesn’t change in its position either inwards or outwards – rather, if released, will move tangentially away – thus Fcp and Fcf are balanced v1 Fcp Fcf

  17. The equations • So how do we get the numbers? • The equation for centripetal acceleration is determined by looking at the velocity vectors at an instant and another measureable quantity in the motion of the circle – the radius

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