Circular M o ti o n Review Questi o n What is the tangential speed of a passenger on a Ferris wheel that has a radius of 10 m and rotates once in 30 s? Hint: Recall from geometry C = 2  r and from linear motion speed = distance/time r = 10 m

Chapter 8 – R o tati o nal M o ti o n R o tati o nal Inertia

Inertia vs. R o tati o nal Inertia Inertia –Object at rest tends to stay at rest and an object in motion tends to remain moving in a straight line Rotational Inertia –An object rotating about an axis tends to remain rotating about that axis unless interfered with by some external influence

R o tati o nal Inertia Depends on: –Mass –Mass distribution relative to the axis of rotation Inertia Race… –Solid disk will always win –With the ring, all of its mass is far from the center, giving it a greater rotational inertia The greater the distance between the majority of an objects mass and its axis of rotation, the more rotational inertia it has.  EasyDifficult 

R o tati o nal Inertia Everyday appearances of rotational inertia… Tightrope walker carries a long pole –Majority of the mass is at the ends making it difficult to rotate –If he starts to fall, a tight grip will rotate the pole –Pole resists because of its high rotational inertia –This gives the walker more time to readjust his balance Baseball players “choke up” on the bat –Mass located far from rotational axis –Grasp the bat closer to the mass and it becomes easier to swing Running –You bend your legs when you run, bringing your legs mass closer to the axis of rotation –People with longer legs have a slower stride and vice versa –Animals: The stride of a giraffe vs. the stride of a dachshund

R o tati o nal Inertia The RI of an object also depends on which axis the object is rotated about… Consider a pencil  there are 3 possible choices 1.Axis through the lead 2.Axis through the center of gravity 3.Axis at the eraser 1-3, easiest to hardest

R o tati o nal Inertias f o r C o mm o n Shapes

Example #1 Consider balancing a hammer upright on the tip of your finger. If the head of the hammer is heavy and the handle is long, would it be easier to balance with the end of the handle on you fingertips so that the head is at the top, or the other way around with the head at your fingertips and the end of the handle at the top?

Example #2 It is more difficult to do a sit-up with your hands held behind your head than it is to do a sit-up with your arms stretched out in front of you. Explain why this statement is true.

R o tati o nal Inertia Review Questi o ns 1.Inertia depends on mass; rotational inertia depends on mass and something else. What? 2.Does the rotational inertia of an object differ for different axes of rotation? 3.Which will have the greater acceleration rolling down an incline, a hoop or a solid disk?