首先，我们需要使用Java的GUI库Swing来创建一个窗口，然后在窗口中心画一个圆和一个直角扇形。接着在圆内随机生成一个黑点.最后，当翻转按钮被按下时，将扇形慢慢移到黑点的位置，同时将扇形变为红色，并在控制台输出黑点的坐标和与圆心的角度。

以下是实现代码示例：

import java.awt.Color;
import java.awt.Graphics;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.util.Random;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class FanGame extends JFrame implements ActionListener {
    private static final long serialVersionUID = 1L;
    private JButton flipBtn;
    private FanPanel fanPanel;
    private Random rand;

    public FanGame() {
        super("Fan Game");
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setSize(400, 400);
        setResizable(false);
        setLocationRelativeTo(null);

        rand = new Random();
        fanPanel = new FanPanel();
        flipBtn = new JButton("Flip");
        flipBtn.addActionListener(this);

        JPanel contentPane = new JPanel();
        contentPane.setBackground(Color.WHITE);
        contentPane.setLayout(null);

        fanPanel.setBounds(0, 0, 400, 400);
        flipBtn.setBounds(160, 360, 80, 30);

        contentPane.add(fanPanel);
        contentPane.add(flipBtn);

        setContentPane(contentPane);
        setVisible(true);
    }

    public static void main(String[] args) {
        new FanGame();
    }

    @Override
    public void actionPerformed(ActionEvent e) {
        if (e.getSource() == flipBtn) {
            fanPanel.flipToBlackDot();
        }
    }
}

class FanPanel extends JPanel {
    private static final long serialVersionUID = 1L;
    private int centerX;
    private int centerY;
    private int radius;
    private int fanAngle;
    private int fanStartAngle;
    private int fanEndAngle;
    private int fanStep;
    private int fanX1;
    private int fanY1;
    private int fanX2;
    private int fanY2;
    private int dotX;
    private int dotY;
    private boolean isFanFlipped;
    private Random rand;

    public FanPanel() {
        rand = new Random();
        centerX = 200;
        centerY = 200;
        radius = 150;
        fanAngle = 0;
        fanStartAngle = 45;
        fanEndAngle = 225;
        fanStep = 5;
        fanX1 = centerX;
        fanY1 = centerY;
        fanX2 = centerX;
        fanY2 = centerY - radius;
        isFanFlipped = false;
        dotX = centerX;
        dotY = centerY;
    }

    public void flipToBlackDot() {
        if (!isFanFlipped) {
            int angle = rand.nextInt(360);
            double radian = Math.toRadians(angle);
            dotX = (int) (centerX + (radius - 10) * Math.cos(radian));
            dotY = (int) (centerY - (radius - 10) * Math.sin(radian));
            fanAngle = angle + 90;
            isFanFlipped = true;
            repaint();
            System.out.println("Black Dot: (" + dotX + ", " + dotY + ")");
            System.out.println("Fan Angle: " + fanAngle);
        }
    }

    @Override
    public void paintComponent(Graphics g) {
        super.paintComponent(g);

        g.setColor(Color.BLACK);
        g.drawOval(centerX - radius, centerY - radius, radius * 2, radius * 2);

        g.setColor(Color.RED);
        if (isFanFlipped) {
            g.fillArc(centerX - radius, centerY - radius, radius * 2, radius * 2, fanStartAngle, fanAngle - fanStartAngle);
        } else {
            g.fillArc(centerX - radius, centerY - radius, radius * 2, radius * 2, fanStartAngle, fanEndAngle - fanStartAngle);
        }

        g.setColor(Color.BLACK);
        g.fillOval(dotX - 5, dotY - 5, 10, 10);
    }
}