Question

At t=0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 3.0 rad/s. Three seconds later it has turned through 8.0 complete revolutions. What is the angular acceleration of this wheel?

A. 7 rad/s^2
B. 16 rad/s^2
C. 9 rad/s^2
D. 4 rad/s^2
E. 13 rad/s^2

Answer 1

Use the following equation:\[\theta = \omega t +\frac{ 1 }{ 2 }\alpha t ^{2}\]

Answer 2

My professor still hasn't gone over this chapter but I am doing my HW early. Can you explain what each of those suppose to mean?

Answer 3

Ok. θ is the total angular displacement. 1 full revolution would give:\[\theta=2\pi=360°\] ω is the angular velocity. α is the angular acceleration, and t is time. Note that in the problem, you're given the total angular displacement (8 complete revolutions), the initial angular velocity, ω (3.0 rad/s), and t (3 seconds). Do you see how to solve the problem, now?

Note how the equation is very similar to an equation you've likely seen earlier:\[x=vt + \frac{ 1 }{ 2 }at ^{2}\], an equation used in linear motion. You'll find that virtually all rotational motion equations have a linear motion analogue.

Answer 4

So the equation is \[8=3*3+.5\alpha3^2\] Right?

Answer 5

Almost. θ is 8 "full revolutions." How many radians are in a full revolution?

Answer 6

16pi?

Answer 7

Yes.

Answer 8

so the angular accel is 9.17, which would be C. Correct?

Answer 9

Yup.

Answer 10

Thanks!

Answer 11

De nada.