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.
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
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