A playground merry go round has a mass of 125kg and radius of 1.6m is rotating with a frequency of 0.42 rev/s. What is the magnitude of its angular velocity in radians per second after a 25kg child gets onto in be grabbing by its edge? The child is initially at rest.
angular momentum is conserved
initial ang. mom. of ride = final ang. mom. of ride + ang. mom. of child
where did mom came from
AngularMomentumInitial=AngularMomentumFinal+AngularMomentumChild
No Moms involved.
The child is not a hoop. The child is a point mass. I= m r^2
To find the magnitude of the angular velocity in radians per second after the child gets onto the merry go round, we need to apply the principle of conservation of angular momentum.
First, let's find the initial angular momentum of the merry go round before the child gets on. The formula for angular momentum is given by:
L = Iω
Where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia for a solid disk rotating about its center is given by:
I = (1/2) * m * r^2
Where m is the mass of the disk and r is the radius.
Substituting the given values, the initial angular momentum of the merry go round before the child gets on is:
L_initial = (1/2) * (125 kg) * (1.6 m)^2 * (0.42 rev/s)
Next, let's find the final angular momentum after the child gets on. Since the child is initially at rest, their initial angular momentum is zero.
The total angular momentum after the child gets on is the sum of the initial angular momentum of the merry go round and the final angular momentum of the child. This can be expressed as:
L_total = L_initial + L_child
Rearranging the equation, we get:
L_child = L_total - L_initial
Now, let's find the final angular momentum:
L_total = I_total * ω_final
The total moment of inertia, I_total, is the sum of the moment of inertia of the merry go round and the child, which can be calculated as:
I_total = (1/2) * (125 kg) * (1.6 m)^2 + (25 kg) * (1.6 m)^2
Finally, we can find the final angular velocity, ω_final, by rearranging the equation for angular momentum:
ω_final = L_total / I_total
Substituting the known values, we can calculate the final angular velocity in radians per second.
since L=Iw, I=aMR^2, and a for disk(merry go round) a=1/2 and hoop(how child is moving on the merry go round) a=1
0.42rev/s =2.638937829 rad/s
I've tried
1/2(125)(1.6^2)(2.638937829)=1(125+25)(1.6^2)w
w=1.099
but the answer came out wrong