Solving Angular Rotation Homework: Question b, c & d

[ataglance05]

Homework Statement

A 1kg engine rotates at 1 rad/sec about a point on a 3meter wire. The engine produces an acceleration of 1 rad/sec^2 and is fird for 2 minutes.

a) What is the ω at the end of 2 minutes?
b) what's the tension in the wire at the end of 2 min.?
c) how far will the engine travel in meters while it's accelerating?
d) what's the Kinetic Energy of the engine after it shuts down?

Homework Equations

a)ω=radius/Time or ω= θ/Time
B) ?
c) S=rθ
θ= ωi(T)+1/2αT^2
d) KE=1/2(Ι)(angluar acceleration)(T)^2
Ι=1/2mr^2

The Attempt at a Solution

a) ω=radius/Time
ω=3/120= 0.25 rad/sec
b)?
c) ?
d) Ι=1/2mr^2
Ι=1/2(1)(3)^2= 3

KE=1/2(Ι)(angluar acceleration)(T)^2
KE=1/2(3)(1)(120)^2
KE=21600 J

need help with b&c and with corroborating a&d!
thanks!

 

[andrevdh]

a) The engine is experiencing a constant angular acceleration, $$\alpha$$, while it is fired. The constant angular acceleration equations look similar to the constant linear acceleration equations:

$$\omega = \omega _i + \alpha t$$

b) Use the final angular speed to calculate the centripetal force that the engine is experiencing, this will be the tension in the wire.

c) your equations should do the trick

d) I think the kinetic energy is given by

$$EK = \frac{1}{2}I \omega ^2$$