Angular Velocity: Calculate New Speed After 4 People Step On

[melissa_y]

A 5.4m diameter merry-go-round is rotating freely with an angular velocity of 0.730 rad/s. Its total moment of inertia is 1665kg*m2. Four people standing on the ground, each of mass 60.8kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now? Use units of "rad/s".

 

[himanshu121]

[HINT] :: No external torque use conservation of Angular momentum ::

 

[thepatientmental]

To calculate the new angular velocity, we can use the conservation of angular momentum equation:

I₁ω₁ = I₂ω₂

Where I₁ and ω₁ are the initial moment of inertia and angular velocity, and I₂ and ω₂ are the final moment of inertia and angular velocity.

Substituting the given values, we have:

1665kg*m² * 0.730 rad/s = (1665kg*m² + 4*60.8kg*5.4m²) * ω₂

Solving for ω₂, we get:

ω₂ = (1665kg*m² * 0.730 rad/s) / (1665kg*m² + 4*60.8kg*5.4m²)

= 0.713 rad/s

Therefore, the new angular velocity of the merry-go-round after 4 people step on is 0.713 rad/s. This represents a decrease in angular velocity, as the added mass causes an increase in moment of inertia.