A merry-go-round has an angular velocity of 5.20 rad/s. A ribbon is tied at the end of one of the arms and it has speed of 3.60 m/s. At what distance is the ribbon from the center of the merry-go-round?
as with arc length and angle, s=rθ,
ds/dt = r dθ/dt
v = rω
so, plug in your numbers
To find the distance of the ribbon from the center of the merry-go-round, we can use the relationship between angular velocity and linear velocity.
The linear velocity of the ribbon is given as 3.60 m/s. This linear velocity is actually the tangential velocity at the location of the ribbon. The tangential velocity is the linear velocity of an object moving along the circumference of a circle.
The angular velocity is given as 5.20 rad/s. Angular velocity is the rate at which an object rotates around an axis.
The relationship between linear velocity (v), angular velocity (ω), and radius (r) is given by the equation:
v = ω * r
Where:
v = linear velocity
ω = angular velocity
r = radius
We can rearrange this equation to solve for the radius:
r = v / ω
Substituting the given values:
r = 3.60 m/s / 5.20 rad/s
Calculating this:
r = 0.692 m
Therefore, the distance of the ribbon from the center of the merry-go-round is approximately 0.692 meters.