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Haplosciences.com |
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CIRCULAR MOTION: worksheet |
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A) A circle covers 360 degrees or 2 Π radians Can you convert 90 degrees = ____________ radians ? 30 degrees = ______________ radians 10 degrees = _____________ radians Hint: 360/ (2 Π) = 90 / X
B) The distance around a circle (circumference) d = 2 Π R (in meters) with R the radius. 2 Π being the angle covered by the circle in radians (or 360 degrees). So to find the distance around an 2 Π angle, you must multiply the radius R (m) by the angle in radians. Right ? So If you take just a slice of the circle, (R = 3cm) let’s say a 60 degrees piece: |
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Find the distance D between A and B.
D = AB= _____ cm
(convert 30 degrees in radians first) |
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C) If You cut a 45 degrees slice out, what is the distance around ? D= ___________ cm 45 degrees is 1/8 (one eighth) of a circle. Find: 2 Π R / 8 (that is 1/8 of the circumference) = _________ cm Do you get the same number ? ______________
D) Let’s cut 30 degrees slice. D = _________ cm Do you find half what you found in B ? _________
E) extra credits: (show the work) Trace a line between A and B ( WITH A RULER) Can you find the length of the segment AB ? AB = ____________ cm (hint: The triangle OAB is an isosceles triangle. Half of it is a right angle triangle. Use tangent to find AB)
F) So you just showed that in a slice of circle, the arc AB = R Θ (Θ IS IN RADIANS !)
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G) The direction of the acceleration of an object moving along a circular path is toward the center of the circle. (if the observer is at rest and not on the moving object) This acceleration is called __________________________________.
H) the direction of acceleration is _________________the force
I) Acceleration is directed toward the ________________ of a circular path.
J) advanced: just read. You have learned that : AB = R Θ AB is the linear distance and Θ the angle in radians. From this relation, V = R ω with ω = ΔΘ / t , ω is the rotational speed in rad/s, t is the time in s, R is the radius (cm or m), Vis the orbital speed. Like wise, a T= R α aT is the tangential acceleration increasing the orbital speed (not to confuse with the centripetal acceleration ac, perpendicular to the orbital velocity. aT has the same direction as the orbital velocity) and is the angular acceleration. (the object is going in circle faster and faster unlike the Moon whose aT is 0 since the orbital speed is constant.
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Let’s say a ant is moving from A to B in 5 seconds at a constant speed following the arc (R = 3cm and Θ = 50 degrees) . The orbital speed (or tangential ) of the ant = AB / t = ______________. (rremember you need to convert Θ in radians and multiply by R to get AB) |
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REMEMBER THAT FROM NOW:
ARC LENGH (m or cm) = RADIUS (9m or cm) x ANGLE IN RADIANS
ANGLE in RADIANS = ANGLE in DEGEES x (2 Π /360 ) |
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