second condition of equilibruim,rigid bodies motion..help?

Question

question....please help me

At t=0 the current to a dc electronic motor is reversed resulting in an angular displacement of the motor shaft given by theta(t) = (250 rad/s)t - 20 rad/s^2)t^-(1.50 rad/s^3)t^3.
a.) at what time is the angular velocity of the motor shaft zero? b.) CAlculate the angular acceleration at the instant that the motor shaft has zero angular velocity. c.) How many revolutions does the motor shaft turn trough between the time when the current is reversed and rhe instant when the angular velocity is zero? d.) How fast was the motor shaft rotating at t=0,when the current was reversed?

thanks really for the help.:)

Answer 1

a) take derivative to get angular velocity and put it equal to zero. Solve for t. Is that a typo?? t^ ??? is it t^2 ???? If t^2 then derivative = 250 -40t -4.5 t^2. use quadratic formula to solve for t

b) for aceleration, take the derivative of the derivative above

= -40 -9t. Substitute time from a)

c) Find theta for the given time. Divide by 2Pi to get revs

d) Put t=0 into first derivative. I assume how fast means angular velocity???

Tough questions !!

Answer 2

a) Take the derivative with respect to time of your expression for theta. This will give you an expression for the angular velocity as a function of time. Set that equal to zero and solve for t.

b) Take the derivative with respect to time of your expression for angular velocity and you'll have an expression for angular acceleration. Plug in the time and solve for the angular acceleration.

c) Plug the time you got in part a into the equation for theta. This will give you the number of radians the shaft rotated through. Remember that 2pi radians equals one revolution, and convert to revolutions.

d) Plug t=0 into your expression for angular velocity and solve.

Answer 3

Do you want this messy melted ice cream to be calculated?
theta(t) = (250 rad/s)t - 20 rad/s^2)t^-(1.50 rad/s^3)t^3.