Question

A disk of radius 10 cm speeds up from rest. it turns 60 radians reaching an angular velocity of 15 rad/s. what was the angular acceleration?
b. how long did it take the disk to reach this velocity?​

Answer 1

Answer:

a) α = 1.875 $\frac{rad}{s^{2} }$

b) t = 8 s

Explanation:

Given:

ω1 = 0 $\frac{rad}{s}$

ω2 = 15 $\frac{rad}{s}$

theta (angular displacement) = 60 rad

*side note: you can replace regular, linear variables in kinematic equations with angular variables (must entirely replace equations with angular variables)*

a) α = ?

(ω2)^2 = (ω1)^2 + 2α(theta)

$15^{2}$ = $0^{2}$ + 2(α)(60)

225 = 120α

α = 1.875 $\frac{rad}{s^{2} }$

b)

α = (ω2-ω1)/t

t = (ω2-ω1)/α = (15-0)/1.875 = 8

t = 8 s