Physics Study Guide Question?

Question

I'm trying to study for my physics test, but I can't figure out part B (and I guess technically C or D) of this question:

2.  Flywheels represent one method of storing energy for use during peak loads, and have seen limited use in buses.  In one configuration a carbon-fiber cylinder of radius r = 0.5 m and moment of inertia I = 200 kg m2 operates at an angular speed of 24,000 rpm at full capacity.  (a) (5 points)  Calculate the energy stored in the flywheel.
(b) (5 points)  Assuming that the torque applied in accelerating the wheel is 2000 N m, the time required to reach its maximum angular velocity is
(c) (5 points)  The number of revolutions the flywheel rotates in reaching this velocity is
(d) (4 points)  At full speed the acceleration of a particle on the outer surface of the cylinder is

I solved part A by doing 24000 rpm * 2 * pi/60 = ~2512
KE = 1/2 * I * w^2
.5  * 2512^2 * 200 = 6.31e8

But I have no idea how to do the rest. Anyone have any ideas?

Thanks!

Big Daddy · Accepted Answer

(a) is numerically correct, but please keep your units on figures.  

For (b), sometimes it's easier to remember the translational equations and convert.  If you knew mass, force, and speeds, could you figure out how long to accelerate?  Sure.  From rest:
v = a t
v = (F/m) * t
t = v m / F

Turning that into rotational concepts:
t = omega I / tau
t = 2513 radians/s  * 200 kg m^2 / 2000 N m
t = 251s

(c) is similar.  
x = .5 a t^2
x = .5 (F/m) t^2
theta = .5 (tau/I) t^2
You have (F/tau), (m/I) and t, so solve for (x/theta), then convert radians to revolutions

(d) is just asking for centripetal acceleration of the point.  You have r and omega (from the problem), which is all you need.
a = omega^2 r

Physics Study Guide Question?

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