# Lec7 - Today Chapter 8 Rotation Chapter 8 Rotational Motion...

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Today Chapter 8: Rotation

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Chapter 8: Rotational Motion If you ride near the outside of a merry-go-round, do you go faster or slower than if you ride near the middle? It depends on whether “faster” means - a faster linear speed (= speed) , ie more distance covered per second, or - a faster rotational speed (=angular speed, ϖ ), i.e. more rotations or revolutions per second. The linear speed of a rotating object is greater on the outside, further from the axis (center), but the rotational speed is the same for any point on the object – all parts make the same # of rotations in the same time interval.
More on rotational vs tangential speed The faster the ϖ , the faster the v in the same way (e.g. merry-go-round), i.e. v ~ ϖ . - ϖ doesn’t depend on where you are on the merry-go-round, but v does: i.e. v ~ r directly proportional to Same RPM ( ϖ ) for all these people, but different tangential speeds. He’s got twice the linear speed than this guy. For motion in a circle, linear speed is often called tangential speed

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A carnival has a Ferris wheel where the seats are located halfway between the center and outside rim. Compared with a Ferris wheel with seats on are on the outside rim, your angular speed while riding on this Ferris wheel would be A) more and your tangential speed less. B) the same and your tangential speed less. C) less and your tangential speed more. D) None of the above Answer: B Same # cycles per second i.e. same angular speed, but less distance covered each second, so less tangential speed Clicker Question
Example and Demo: Railroad train wheels Model: two tapered cups stuck together and rolling along meter sticks Now, if you tape two together, at their wide ends, and let them roll along two meter sticks (“tracks”), they will stay stably on the tracks. Why? When they roll off center, they self-correct: say they roll to the left, then the wider part of the left cup and the narrower part of the right cup are on the tracks, causing rolling back to the right, since the left cup has larger tangential speed. First note that if you roll a tapered cup along a table, it follows a circle because the wide part moves faster than the narrow part. (Larger v so more distance covered by the wide end). Railroad wheels act on this same principle!

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Rotational Inertia An object rotating about an axis tends to remain rotating about the same axis, unless an external influence ( torque , see soon) is acting. (c.f. 1 st law) The property to resist changes in rotational state of motion is called rotational inertia , or moment of inertia, I . Depends on mass , as well as the distribution of the mass relative to axis of rotation – largest if the mass is further away from the axis Eg. DEMO: Spinning a pencil with globs of play-doh on it – if the globs are near the ends of the pencil, it is harder to spin, than if the globs are nearer the middle.
Eg. Tight-rope walker carries a pole to increase his rotational inertia - if he starts to wobble, the pole starts to rotate but its

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Lec7 - Today Chapter 8 Rotation Chapter 8 Rotational Motion...

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