Radial force on a particle with circular motion

[Lee333]

A particle of mass 0.014 kg is traveling on a radius 0.9m at a rotational velocity of 36+5*t rad.s-1.


How many revolutions does the particle go thorugh in 4.8 seconds? [revs]


What is the radial force on the particle at 4.8 seconds? [N] (Hint: consider directions)
(question I'm stuck on)


What is the absolute magnitude of force on the particle at 4.8 seconds? [N]



We know that the radial acceleration = v^2/r



To find the amount of revolutions I simply integrated the rotational velocity with respect to time, and found that the particle rotated 230.4 radians or 36.69 revs.

The second question is the question that I seem to be getting wrong. The way I tried to solve it was by firstly finding the rotational velocity after 4.8 seconds:
w = 36+5*4.8
= 60 rad/s

thus we know that the translational velocity is:
v= rw
= 60*0.9
= 54 m/s

we know that the radial acceleration, ra, can be defined by:
ra = v^2/r
= 54^2/0.9
= 3240

thus the radial force, Fr, is:
Fr = m*ra
=0.014*3240
=45.36 N

the above question i am getting wrong for some reason. any help would be appreciated




For the final question we know that the angular acceleration is 5 rad/s^2
this means the linear acceleration of the particle is 4.5 m/s.

we know the translational force will be Ft=m*a
Ft = 0.014*4.5
= 0.063

So we can work out the total magnitude of the force like so:
F_tot = sqrt(0.063^2+45.36^2)
= 45.36

 

[BruceW]

hi lee, welcome to physicsforums :)
Your answer looks good to me. Maybe they also wanted the direction of the radial force at that time.

 

[Lee333]

Thanks for answering, I think its got something to do with the consider directions hint, but I am not sure what I've done wrong. I don't think they want the direction of the radial force because they didn't give a starting position for the particle, so we don't know the direction of the force.

 

[BruceW]

ah, that's true, they don't give the starting position. Then maybe you are meant to give the direction of the radial force, compared to its direction at t=0 ? This is a bit of a stretch, but I can't imagine what else they want for the answer...