course Phy 121 I got to a certain point in the assignment and realize that I need some advice because I keep going in the wrong direction trying to figure this stuff out--either that or I'm trying too hard! ú¥×‹rõÊ¡öÙ“ÃÞœŠÇÆ|^ÑûœÅ·Û”‘¯
......!!!!!!!!...................................
06:53:51 `q001. Note that this assignment contains 15 questions. If an object moves a distance along the arc of a circle equal to the radius of the circle, it is said to move through one radian of angle. If a circle has a radius of 40 meters, then how far would you have to walk along the arc of the circle to move through one radian of angle? How far would you have to walk to move through 3 radians?
......!!!!!!!!...................................
RESPONSE --> ? confidence assessment: 0
.................................................
úå†çÙ}ÉyèÁæ®Ëœ¿ûôìž`³© assignment #029 029. Radian measure of angle; angular position, angular velocity Physics II 03-30-2008
......!!!!!!!!...................................
07:11:01 `q001. Note that this assignment contains 15 questions. If an object moves a distance along the arc of a circle equal to the radius of the circle, it is said to move through one radian of angle. If a circle has a radius of 40 meters, then how far would you have to walk along the arc of the circle to move through one radian of angle? How far would you have to walk to move through 3 radians?
......!!!!!!!!...................................
RESPONSE --> The arc is determined by the distance between two points on the edge of the circle, which is equivalent to the radius of the circle. If the arc (l) is equal to the radius (r), then the angle within the circle ('theta) is going to be equal to 1 radian (i.e. 1 rad) So 'theta = l ÷ r 'theta = 40 m / 1 r 'theta = 40 meters For 3 radians, just multiply 40 meters by 3 radians and the answer is 120 meters. confidence assessment: 2
.................................................
......!!!!!!!!...................................
07:11:18 Since 1 radian of angle corresponds to the distance along the arc which is equal to the radius, if the radius of the circle is 40 meters then a 1 radian angle would correspond to a distance of 40 meters along the arc. An angle of 3 radians would correspond to a distance of 3 * 40 meters = 120 meters along the arc. Each radian corresponds to a distance of 40 meters along the arc.
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 2
.................................................
......!!!!!!!!...................................
07:16:19 `q002. On a circle of radius 40 meters, how far would you have to walk to go all the way around the circle, and through how many radians of angle would you therefore travel? Through how many radians would you travel if you walked halfway around the circle? Through how many radians would you travel if you walked a quarter of the way around the circle?
......!!!!!!!!...................................
RESPONSE --> Well, there are 360 degrees in a circle. If we are still referring to the previous problem, where 1 rad = 40 meters, all we would have to do to determine the number of radians traveled is divide 360 degrees by 40 meters. Then the answer would be 9 radians. Halfway around the circle would be 4.5 rad A quarter of the distance would correspond to 2.25 rad confidence assessment: 1
.................................................
......!!!!!!!!...................................
07:20:54 The circumference of a circle is the product of `pi and its diameter, or in terms of the radius r, which is half the diameter, C = 2 `pi r. The circumference of this circle is therefore 2 `pi * 40 meters = 80 `pi meters. This distance can be left in this form, which is exact, or if appropriate this distance can be approximated as 80 * 3.14 meters = 251 meters (approx). The exact distance 2 `pi * 40 meters is 2 `pi times the radius of the circle, so it corresponds to 2 `pi radians of arc. Half the arc of the circle would correspond to a distance of half the circumference, or to 1/2 ( 80 `pi meters) = 40 `pi meters. This is `pi times the radius so corresponds to `pi radians of angle. A quarter of an arc would correspond to half the preceding angle, or `pi/2 radians.
......!!!!!!!!...................................
RESPONSE --> My mind just wasn't flexible enough self critique assessment: 1
.................................................
......!!!!!!!!...................................
07:49:23 `q003. On a circle of radius 6 meters, what distance along the arc would correspond to 3 radians? What distance would correspond to `pi / 6 radians? What distance would correspond to 4 `pi / 3 radians?
......!!!!!!!!...................................
RESPONSE --> I think the answer to the first question would be 18.84 meters. I determined this by the formula l = 2 'pi r (arc = 2 'pi * radian, since we are taking the entire circumference of the circle into account)
.................................................
......!!!!!!!!...................................
07:52:35 3 radians along the arc would correspond to an arc distance of 3 times the radius, or 3 * 6 meters, or 18 meters. `pi / 6 radians would correspond to `pi / 6 times the radius, or `pi / 6 * 6 meters = `pi meters. 4 `pi / 3 radians would correspond to 4 `pi / 3 * 6 meters = 8 `pi meters.
......!!!!!!!!...................................
RESPONSE --> Maybe I'm trying too hard, I don't know...I need an evaluation... self critique assessment: 1
................................................."