Question
Genesis is riding a merry-go-round at a distance of 4.2m from the vertical axis of rotation. Assuming that the merry go round is moving anti clockwise when viewed from above with an angular speed at a rare of 0.28 radian per second square. Calculate Genesis' translational velocity, his rotational acceleration, his translational acceleration and the magnitude of Genesis'acceleration
Answers
GPT 3.5
The translational velocity of an object on a rotating merry-go-round can be found using the equation:
v = r * ω
where:
v = translational velocity
r = distance from the axis of rotation
ω = angular speed
Given:
r = 4.2m
ω = 0.28 rad/s
v = 4.2m * 0.28 rad/s = 1.176 m/s
The rotational acceleration can be found using the equation:
α = r * α
where:
α = rotational acceleration
Given:
r = 4.2m
α = 0.28 rad/s^2
α = 4.2m * 0.28 rad/s^2 = 1.176 m/s^2
The translational acceleration can be found by using the equation:
a = r * α
Given:
r = 4.2m
α = 1.176 m/s^2
a = 4.2m * 1.176 m/s^2 = 4.9632 m/s^2
The magnitude of Genesis' acceleration can be calculated using the equation:
a_total = √(a^2 + v^2)
Given:
a = 4.9632 m/s^2
v = 1.176 m/s
a_total = √(4.9632^2 + 1.176^2)
a_total = √(24.6326 + 1.3846)
a_total = √26.0172
a_total = 5.101 m/s^2
Therefore, Genesis' translational velocity is 1.176 m/s, his rotational acceleration is 1.176 m/s^2, his translational acceleration is 4.9632 m/s^2, and the magnitude of Genesis' acceleration is 5.101 m/s^2.
v = r * ω
where:
v = translational velocity
r = distance from the axis of rotation
ω = angular speed
Given:
r = 4.2m
ω = 0.28 rad/s
v = 4.2m * 0.28 rad/s = 1.176 m/s
The rotational acceleration can be found using the equation:
α = r * α
where:
α = rotational acceleration
Given:
r = 4.2m
α = 0.28 rad/s^2
α = 4.2m * 0.28 rad/s^2 = 1.176 m/s^2
The translational acceleration can be found by using the equation:
a = r * α
Given:
r = 4.2m
α = 1.176 m/s^2
a = 4.2m * 1.176 m/s^2 = 4.9632 m/s^2
The magnitude of Genesis' acceleration can be calculated using the equation:
a_total = √(a^2 + v^2)
Given:
a = 4.9632 m/s^2
v = 1.176 m/s
a_total = √(4.9632^2 + 1.176^2)
a_total = √(24.6326 + 1.3846)
a_total = √26.0172
a_total = 5.101 m/s^2
Therefore, Genesis' translational velocity is 1.176 m/s, his rotational acceleration is 1.176 m/s^2, his translational acceleration is 4.9632 m/s^2, and the magnitude of Genesis' acceleration is 5.101 m/s^2.