Question

after hillary realized her clock was running 30 minutes fast, she used a knob on the clock to turn the minute hand back 30 minutes. which describes the rotation of the minute hand?

\\(180^\circ\\) clockwise rotation
\\(90^\circ\\) clockwise rotation
\\(90^\circ\\) counterclockwise rotation
\\(180^\circ\\) counterclockwise rotation

Explanation:

Determine the direction of rotation

To turn a clock hand back (earlier in time), we must rotate it in the direction opposite to its normal movement. Since a clock normally runs clockwise, turning the hand back requires a counterclockwise rotation.

Calculate the angle of rotation

A full circle represents \(360^\circ\) and corresponds to \(60\) minutes on a clock face.

$$ \text{Angle per minute} = \frac{360^\circ}{60} = 6^\circ/\text{minute} $$

For a change of \(30\) minutes:

$$ \text{Angle} = 30 \times 6^\circ = 180^\circ $$

Combine direction and angle

Combining the counterclockwise direction with the calculated angle of \(180^\circ\) yields a \(180^\circ\) counterclockwise rotation.

Answer:

• (A) \(180^\circ\) clockwise rotation
• (B) \(90^\circ\) clockwise rotation
• (C) \(90^\circ\) counterclockwise rotation
• (D) \(180^\circ\) counterclockwise rotation (Correct answer)