Question

Angular velocity of a minute hand clock is-
1. \(\frac{π}{60} \:rad/s\)
2. \(\frac{π}{90} \:rad/s\)
3. \(\frac{π}{1800} \:rad/s\)
4. \(\frac{π}{1200} \:rad/s\)

Answer 1

Correct Answer - Option 3 : \(\frac{π}{1800} \:rad/s\)

The correct answer is option 3) i.e. \(\frac{π}{1800} \:rad/s\)

CONCEPT:

• Angular velocity is the velocity associated with objects moving on a curved path.
  • While on a curved path, the displacement is the change in angle about the point of rotation or curved motion.

Angular velocity, \(ω =\frac{angle}{time} =\frac{d\theta}{dt}\)

• The tangent to any point on the curved path gives the direction of the linear velocity of the object at that point.
• The angular velocity ω is related to the linear velocity of an object v by the equation

v = rω 

Where r is the radius of the curvature.

EXPLANATION:

• Angle covered by the minute hand in one complete rotation: 2π radian

Time taken to cover 2π radian : 1 hour = 3600 seconds

Angular velocity, \(ω =\frac{angle}{time} =\frac{d\theta}{dt} = \frac{2\pi}{3600} = \frac{\pi}{1800} \: rad/s\)