Question

a wheel has a constant angular acceleration of 3.0 rad/s2. during a certain 4.0s interval it turns through an angle of 120 rad. assuming that the wheel started from rest, how long has it been in motion at the start of this 4 s interval

Answer 1

8 s

Step-by-step explanation:

We are given that

Acceleration=
`\alpha=3 rad/s^2`

Time, t=4 s

Angle,
`\theta=120 rad`

Initial angular velocity,
`\omega_0=0 rad/s`

Let
`\omega` be the velocity at the start of this 4 s interval

We know that

`\theta=\omega_0t+(1)/(2)\alpha t^2`

Using the formula

`120=4\omega+(1)/(2)(3)(4)^2`

`120=4\omega+24`

`120-24=4\omega`

`4\omega=96`

`\omega=(96)/(4)=24rad/s`

`t=(\omega-\omega_0)/(\alpha)=(24-0)/(3)=8 s`

t=8 s