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

4.25 s

Step-by-step 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 +
`(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