Question

A wheel has a constant angular acceleration of 1.8 rad/s2. During a certain 4.0 s interval, it turns through an angle of 45 rad. Assuming that the wheel started from rest, how long had it been in motion before the start of the 4.0 s interval?

Answer 1

Answer:

4.25 s

Explanation:

Given:

angular acceleration'α'=  1.8 rad/s²

angle 'θ'= 45 rad

time 't'= 4s

initial angular velocity '$w_{o}$'=0$rad^{-1}$

as we know that,

θ= $w_{1}$t + $\frac{1}{2} \alpha t^{2}$

45 = 4 $w_{1}$ + (0.5 x 1.8 x 16)

45- 14.4 = 4 $w_{1}$

30.6 = 4 $w_{1}$

$w_{1}$= 7.65 $rad^{-1}$

Next is to find t by using the equation

$w_{1}$ =  $w_{o}$ + $\alpha t_{1}$

7.65= 0 + (1.8)$t_{1}$

$t_{1}$= 7.65/1.8

$t_{1}$= 4.25 s

Therefore, At the start of 4s interval the motion is at 4.25 second