Question

A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s2. What is its angular speed after it has turned through an angle of 628 radians

Answer 1

Answer:

97.96 $\frac{rad}{s}$

Explanation:

The initial angular velocity is $w_{0}$ = 126 rad / s.

The constant angular deceleration is 5.00 rad / s2.

The constant angular deceleration is, by definition: dw / dt.

$\frac{dw}{dt}=-5 \frac{rad}{s^{2} }$

Separating variables

$dw=-5 dt$

Integration (limits for w: 0 to W0; limits for t: 0 to t)

$w= w_{0}-5t$

W is by definition $\frac{d\alpha }{dt}$, where $\alpha$ is the angle.

$\frac{d\alpha}{dt}=w_{0} -5t$

Separating variables

$d\alpha=(w_{0} -5t )dt$

Integration (limits for $\alpha$: 0 to 628; limits for t: 0 to t)

$\alpha =w_{0}t-(\frac{5}{2})t^{2}$

$128=126t-(\frac{5}{2})t^{2}$

Put in on the typical form of a quadratic equation:

$\frac{5}{2}t^{2}-126t+628=0$

Solve by using the quadratic equation formula and discard the higher result because it lacks physical sense.

t=5.608 s

Evaluate at this time the angular velocity:

$w(t=5.608)=126-5*5.608$

$w(5.608)=97.96 \frac{rad}{s}$