A dog sits 2.1 m from the center of a merry-go-round. If the dog undergoes a 1.4 m/s2 centripetal acceleration, what is the angular speed of the merry-go-round?
5.6kg
To find the angular speed of the merry-go-round, we can use the formula:
angular speed (ω) = √(centripetal acceleration (a) / radius (r))
Given that the dog undergoes a centripetal acceleration of 1.4 m/s^2 and is located 2.1 m from the center of the merry-go-round, we can substitute these values into the formula to find the angular speed.
First, let's calculate the radius (r) of the merry-go-round:
r = 2.1 m
Next, substitute the values into the formula:
ω = √(1.4 m/s^2 / 2.1 m)
Now, divide the centripetal acceleration by the radius to get:
ω = √(0.67 s^-2)
Finally, calculate the square root of 0.67 s^-2:
ω ≈ 0.82 s^-1
So, the angular speed of the merry-go-round is approximately 0.82 radians per second.