Question

The angular quantities: angular displacement, angular velocity, angular acceleration, are defined in a very similar way to the linear quantities. The angular displacement represents the angle through which an object has rotated (the difference between two angular positions). The angular velocity equals the angular displacement divided by the elapsed time. The angular acceleration equals the change in the angular velocity divided by the elapsed time. Suppose an object travels through an angular displacement, Δθ, of 50.9 rad over a time of 4.10 s. What is the average angular velocity, ω?

Answer 1

Hi there!

We can use the following rotational equivalent kinematic equation to solve:

`\omega = (\Delta \theta)/(\Delta t)`

ω = angular velocity (rad/sec)

θ = angular displacement (rad)

t = time (sec)

Plug in the given values:

`\omega = (50.9)/(4.1) = \boxed{12.41 rad/sec}`

Answer 2

Answer: [tex]12.415 rad.s^{-1}[/tex]

Explanation: Angular velocity is the rate of change in angular displacement.

We know that:

Angular velocity,
`\omega= (\Delta \theta)/(t)`....................(1)

where:

• t= time

• 
  `\Delta \theta` = angular displacement in radians

Given that:

• t = 4.10 s

• Δθ = 50.9 radian

Putting the respective values in eq. (1)

`\omega = (50.9)/(4.10)`

`\omega = 12.415 rad.s^(-1)`