1) A CD with a diameter of 12.0 cm starts from rest and with a constant angular
ID: 1965228 • Letter: 1
Question
1) A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec2 acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 seconds with a constant angular deceleration. What is the angular distance traveled by a point 4.00 cm from the center at the time 25.0 seconds from the start?A) 107 rad
B) 193 rad
C) 205 rad
D) 237 rad
E) 274 rad
2 ) A soccer ball of diameter 31 cm rolls without slipping at a linear speed of 2.9 m/s. Through how many revolutions has the soccer ball turned as it moves a linear distance of 16 m?
Explanation / Answer
The CD is going 5 rad/s after 5 sec for seconds 5-20, it is going 5 rad/sec for seconds 20 to 25 is is slowing down at 5/12 rad/s^2. Since we are in radians, we don't need the 4.00 cm. Let's find the 15 seconds at 5 rad/s to see if some of the choices drop out 15s*5 rad/s = 75 rad. This is the bulk of the radians, so it looks like choice A is the correct answer. But let's keep going: In the first five seconds it accelerates from 0 to 5 rad/s The average speed is 2.5 rad/s distance = rate times time = average speed times time = 2.5rad/s*5s = 12.5 rad. We could also solve this by saying distance = 1/2 a t^2 = 1/2*1rad/s^2*25s^2 = 12.5 rad. in the last five seconds it decelerates from 5 rad/s to (5 - 5*5/12)rad/s 5 - 5*5/12 ~ 3 (real answer is 2 11/12) so the average speed in the last five seconds is 4 rad/s distance = rate times time = 4 rad/s*5s = 20 rad. (real answer is a little less) Let's add them up: 75 rad + 12.5 rad + 20 rad = 107.5 rad Choice A is correct 2) 16 m is how many revolutions of a ball with d = 0.31m? circumference = 0.31Pi 16m/0.31Pi = 16 0.31*Pi ~ 1m so we expect the ball to roll once each meter, or 16 times in 16 meters. The linear speed isn't needed to solve this problem.
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