Final answer:
a. The angular speed of the child near the center is 14.74 rad/s, while the angular speed of the child near the edge is 3.66 rad/s.
b. The child near the center moves through an angular distance of 73.7 rad in 5.0 s, while the child near the edge moves through an angular distance of 18.3 rad.
c. The child near the center moves a distance of 57.4 m in 5.0 s, while the child near the edge moves a distance of 57.5 m.
d. The centripetal force experienced by the child near the center is 246.5 N, while the centripetal force experienced by the child near the edge is 963.4 N.
e. The child near the edge has a more difficult time holding on due to experiencing a greater centripetal force.
Step-by-step explanation:
a. To find the angular speed of each child, we can use the formula:
angular speed = translational speed / radius
For the child near the center, the angular speed is:
angular speed = 11.5 m/s / 0.78 m = 14.74 rad/s
For the child near the edge, the angular speed is:
angular speed = 11.5 m/s / 3.14 m = 3.66 rad/s
b. To find the angular distance each child moves in 5.0 s, we can use the formula:
angular distance = angular speed × time
For the child near the center:
angular distance = 14.74 rad/s × 5.0 s = 73.7 rad
For the child near the edge:
angular distance = 3.66 rad/s × 5.0 s = 18.3 rad
c. To find the distance each child moves in 5.0 s, we can use the formula:
distance = angular distance × radius
For the child near the center:
distance = 73.7 rad × 0.78 m = 57.4 m
For the child near the edge:
distance = 18.3 rad × 3.14 m = 57.5 m
d. The centripetal force experienced by each child can be calculated using the formula:
centripetal force = mass × (angular speed)^2 × radius
For the child near the center:
centripetal force = 25.4 kg × (14.74 rad/s)^2 × 0.78 m = 246.5 N
For the child near the edge:
centripetal force = 25.4 kg × (3.66 rad/s)^2 × 3.14 m = 963.4 N
e. The child near the edge has a more difficult time holding on because they experience a greater centripetal force.