A playground merry-go-round has a radius of R = 4.0 m and has a moment of inertia Icm = 7.0 x 10³ kgm² about an axis passing through the center of mass. There is negligible friction about its vertical axis. Two children each of mass m = 25 kg are standing on opposite sides a distance ro= 3.0 m from the central axis. The merry-go-round is initially at rest. A person on the ground applies a constant tangential force of F= 2.5 x10² N at the rim of the merry-go-round for a time At=1.0 x 10¹ s. Lebah R a. What is the magnitude of angular acceleration of the merry-go-round? b. What is the angular speed of the merry-go-round when the person stopped applying the force? c. What is the rotational kinetic energy of the merry-go-round when the person stopped applying the force? d. The two children then walk inward and stop a distance of r1 =1.0 m from the central axis of the merry-go-round. What is the angular velocity of the merry-go- round when the children reach their final position? What is the change in rotational kinetic energy of the merry-go-round when the children reached their final position?

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Chapter1: Units, Trigonometry. And Vectors
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**Description:**

This problem involves a merry-go-round in a playground. It has a radius \( R = 4.0 \, \text{m} \) and a moment of inertia \( I_{\text{cm}} = 7.0 \times 10^3 \, \text{kgm}^2 \). The friction about its vertical axis is negligible.

Two children, each with mass \( m = 25 \, \text{kg} \), stand on opposite sides at a distance \( r_0 = 3.0 \, \text{m} \) from the central axis. Initially at rest, a person applies a constant tangential force \( F = 2.5 \times 10^2 \, \text{N} \) at the rim of the merry-go-round for a duration \( \Delta t = 1.0 \times 10^1 \, \text{s} \).

**Diagram Explanation:**

The diagram illustrates a merry-go-round with two children standing on it. The force \( F \) is shown tangentially at the edge, and the distances \( r_0 \) and \( R \) are marked.

**Questions:**

a. What is the magnitude of angular acceleration of the merry-go-round?

b. What is the angular speed of the merry-go-round when the person stops applying the force?

c. What is the rotational kinetic energy of the merry-go-round when the person stopped applying the force?

d. The two children then walk inward and stop a distance of \( r_1 = 1.0 \, \text{m} \) from the central axis of the merry-go-round. What is the angular velocity of the merry-go-round when the children reach their final position? What is the change in rotational kinetic energy of the merry-go-round when the children reached their final position?
Transcribed Image Text:**Description:** This problem involves a merry-go-round in a playground. It has a radius \( R = 4.0 \, \text{m} \) and a moment of inertia \( I_{\text{cm}} = 7.0 \times 10^3 \, \text{kgm}^2 \). The friction about its vertical axis is negligible. Two children, each with mass \( m = 25 \, \text{kg} \), stand on opposite sides at a distance \( r_0 = 3.0 \, \text{m} \) from the central axis. Initially at rest, a person applies a constant tangential force \( F = 2.5 \times 10^2 \, \text{N} \) at the rim of the merry-go-round for a duration \( \Delta t = 1.0 \times 10^1 \, \text{s} \). **Diagram Explanation:** The diagram illustrates a merry-go-round with two children standing on it. The force \( F \) is shown tangentially at the edge, and the distances \( r_0 \) and \( R \) are marked. **Questions:** a. What is the magnitude of angular acceleration of the merry-go-round? b. What is the angular speed of the merry-go-round when the person stops applying the force? c. What is the rotational kinetic energy of the merry-go-round when the person stopped applying the force? d. The two children then walk inward and stop a distance of \( r_1 = 1.0 \, \text{m} \) from the central axis of the merry-go-round. What is the angular velocity of the merry-go-round when the children reach their final position? What is the change in rotational kinetic energy of the merry-go-round when the children reached their final position?
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