To find the new angular velocity of the merry-go-round after a boy jumps on, you can use the law of conservation of angular momentum. The initial angular momentum is zero since the merry-go-round is at rest, and the final angular momentum is equal to the moment of inertia of the system multiplied by the final angular velocity. By calculating the final angular momentum and substituting the values into the formula, you can determine the new angular velocity of the merry-go-round.
To find the new angular velocity of the merry-go-round, we can use the law of conservation of angular momentum. The initial angular momentum of the system is zero since the merry-go-round is initially at rest. After the boy jumps on, the angular momentum of the system remains constant. We can calculate the initial angular momentum using the formula:
Initial Angular Momentum = Moment of Inertia * Initial Angular Velocity
Since the merry-go-round is initially at rest, the initial angular velocity is zero. So, the initial angular momentum is also zero. After the boy jumps on, the angular momentum is:
Final Angular Momentum = Moment of Inertia * Final Angular Velocity
Using the formula for angular momentum, we can solve for the final angular velocity:
Final Angular Velocity = Final Angular Momentum / Moment of Inertia
Substituting in the given values:
Moment of Inertia = 300 kg · m²
Final Angular Momentum = (Mass of Boy * Radius of Merry-Go-Round + Moment of Inertia of Merry-Go-Round) * Final Angular Velocity
Plugging in the values and solving for the Final Angular Velocity:
Final Angular Velocity = Final Angular Momentum / Moment of Inertia
After substituting the given values, we get the final angular velocity of the merry-go-round.