Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg · m2. The father exerts a force on the merry-go-round perpendicular to its 1.50 m radius to achieve a torque of 375 N · m. (a) Calculate the rotational kinetic energy (in J) in the merry-go-round plus child when they have an angular velocity of 13.4 rpm. J (b) Using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest. revolutions (c) Again, using energy considerations, calculate the force (in N) the father must exert to stop the merry-go-round in six revolutions. N

Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg · m2. The father exerts a force on the merry-go-round perpendicular to its 1.50 m radius to achieve a torque of 375 N · m. (a) Calculate the rotational kinetic energy (in J) in the merry-go-round plus child when they have an angular velocity of 13.4 rpm. J (b) Using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest. revolutions (c) Again, using energy considerations, calculate the force (in N) the father must exert to stop the merry-go-round in six revolutions. N

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Question

Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg · m². The father exerts a force on the merry-go-round perpendicular to its 1.50 m radius to achieve a torque of 375 N · m.

(a)

Calculate the rotational kinetic energy (in J) in the merry-go-round plus child when they have an angular velocity of 13.4 rpm.

(b)

Using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest.

revolutions

(c)

Again, using energy considerations, calculate the force (in N) the father must exert to stop the merry-go-round in six revolutions.

Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.

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