A large merry-go-round completes one revolution every 17.5 s. Compute the acceleration of a child seated on it, a distance of 5.80 m from its center.
First compute the angular velocity of the merry-go-round.
w = 2 pi/17.5 = 0.359 radians/s
centripetal acceleration = R w^2
To compute the acceleration of the child seated on the merry-go-round, we can use the equation for centripetal acceleration:
a = (v^2) / r
where:
a is the acceleration,
v is the linear velocity, and
r is the radius.
First, let's find the linear velocity. Since the merry-go-round completes one revolution every 17.5 seconds, we can calculate the linear velocity as:
v = (2πr) / T
where:
v is the linear velocity,
π is approximately 3.14159,
r is the radius, and
T is the period (time for one complete revolution).
Given:
r = 5.80 m
T = 17.5 s
Substituting these values into the equation, we get:
v = (2π × 5.80) / 17.5
Now, let's find the acceleration using the equation mentioned earlier:
a = (v^2) / r
Plugging in the linear velocity and radius values we obtained earlier, we can calculate the acceleration.