Nonuniform Circular Motion-Find time given r, a-sub-t, V-sub-0

[6maverick6]

Nonuniform Circular Motion--Find time given r, a-sub-t, V-sub-0

Homework Statement

A car turns through 60 degrees while traveling on the circumference of a 35m radius circle. The care is traveling at 8.0 m/s as it enters the turn and maintains a constant tangential acceleration of .4m/s² throughout the turn. How long did it take the car to make the turn?


(A) 2.3s (B) 4.2s (C) 4.9s (D) 8.4s

DATA SUMMARY:
a_t: .4m/s²
V_o: 8.0m/s
R:35m

Homework Equations

a_t=d|v|/dt=.4m/s²

|V|= $$\omega$$ *r

$$\theta$$= $$\omega$$*r

3. The attempt at solution

a_t=d|v|/dt=.4m/s²

|V|=.4t +8.0 (from integrating a_t)

$$\omega$$= (.4t+8.0)/35 (from |V|=$$\omega$$*r)

$$\theta$$= $$\omega$$*r

($$\pi$$/3= ((.4t+8.0)/35)t= (.4/35) + (8.0t/35)

t=4.6

I get the feeling that there's one crucial equation I'm missing...

 

[Fightfish]

$$\theta = \omega_{0} t + \frac{1}{2} \alpha t^{2}$$
should be the equation to be used instead.

$$\theta = \omega t$$ is true only under a constant angular velocity - the general form is $$\theta = \int \omega dt$$
which yields the equation above for constant angular acceleration.

You could also use a translational kinematics approach instead, which I think should be less confusing than rotational dynamics.

 

[6maverick6]

Thank you!

I got it using translational kinematics.