Question

A motorcyclist is riding on a highway. At a certain location he takes a U-turn in 6.25 seconds. The angular velocity during the turn is-
1. 0.5 rad/s
2. 0.2 rad/s
3. 0.3 rad/s
4. 0.4 rad/s

Answer 1

Correct Answer - Option 1 : 0.5 rad/s

The correct answer is option 1) i.e. 0.5 rad/s

CONCEPT:

• Angular velocity is the velocity associated with objects moving in 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, \(ω =\frac{angle}{time} =\frac{dθ}{dt}\)

• 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 motorcyclist in U-turn, θ = 180^∘ = π radian

Time taken to cover π radian,t = 6.25 s

Angular velocity, \(ω =\frac{dθ}{dt} = \frac{\pi}{6.25} =0.5 \: rad/s\)