Physics problem wondering if what I tried was correct please look!!!!!

[edwardraff]

a solid disc of radius 35cm and mass 10kg is turning at 5revolutions/sec. If a tagential foce of 0.8 newtons is applied to the rim then through how man revolutions does the wheel turn before stopping?

What I tried

Torque = I*(angular acceleration
torque = force*lever arm so

angular accerlation is = (force*lever arm)/I = .8*.35/.5(10)(.35)^2 = .6125rev/sec (QUESTION right unit or should it be 1.225pi rad/sec)
so it is losing .6125rev/sec it will take 5/.6125 second to stop right ???? if so 8.126 seconds to come and presuming is is uniform deceleration the averge velocity over those 8.126 seconds was 2.5rev/sec so to find out how many revoulutions it went thur before stopping simply mutiply 8.126sec*avg velocity of 2.5rev/sec and youlearn that it went thru 20.315 revolution before stopping

I am wondering if I am solving this correctly and if not if some one could explain the correct way to solve this proble
Thanks in Advance

 

[SerraYX]

Torque = I (ang accel)
R * F = m * R^2 *angaccel
angaccel = F/(m*R)

Vf^2 = Vinit^2 + 2 (ang accel) (delta theta)

Vf = 0

delta theta = -Vinit^2/(2 * ang accel)

Go from there

 

[edwardraff]

so according to what you say I do 5^2/(2*.6125) = 20.4 which the same number I got minus rounding errors so I am wondering if someone else or you could explain if both methods are correct or if just one is correct

Thanks in Advance

 

[MereMortal]

The units that come out of the equation for angular acceleration are rad/s^2. You seem to put in the right numbers, but come out with a fubared result.

The most straightforward method is the way SerraYX described. The result for the change in angle will be in radians, which you can convert to revolutions for the answer.

Your method is equivalent, but more roundabout in the sense that you use more equations to get the solution. You are trying
to use (here w=angular velocity, alpha=angular acceleration)

w = w_0 + alpha*t

to solve for the time, and then

theta = (w_0 + w)*t/2

to find the angle revolved through. You can combine these equations to get the equation in SerraYX's solution.

 

[edwardraff]

so the answer in terms of revolutions is 20.4/2pi or 3.23revolutions

 

[edwardraff]

??????????

 

[MereMortal]

No. You need to work through the problem using values with correct units. The angular acceleration must be in rad/s^2 and the angular velocity must be in rad/s to use the equations above.

You seemed to set up the angular acceleration properly. I don't understand how you are getting 1.225*pi rad/s for a result. It is numerically wrong, and it has the wrong units. (I just noticed that SerraYX has the wrong value for the moment of inertia for a disc--you have it correct, though. Need that 1/2.)


After you have the acceleration, you can solve solve for the change in angle. Remember, omega must have the right units! You will
end up with the angle in radians. Only then do you convert to revolutions.


Plugging in values in terms of revolutions into the above equations will result in an incorrect answer.