I don't know where to start!!

Question

A wheel initially at rest begins to spin with a constant angular acceleration of 2.0 rad/s^2. Through how many revolutions will it go until its angular velocity reaches 25 rad/s?

Answer 1

Use the kinematic relation for rotational motion:

 

ω_f² - ω_i² = 2αθ

 

Solve for θ in radians, and then divide by 2π to get revolutions.

 

ω_f = 25 rad/s

ω_i = 0  [starts from rest]

α = 2.0 rad/s²  [constant angular acceleration]

θ = total angle that is swept, in radians

θ/(2π) = number of revolutions

 

ω_f² = 2αθ

 

θ = ω_f²/(2α) = (25 rad/s)² / [2(2.0 rad/s²] = 156.25 rad

 

Number of revolutions is

 

θ/(2π) = 156.25 / (2π)