Rotational Motion: Stop a 10 kg Disk in 20 sec

[pradeepk]

Homework Statement

A solid disk of mass 10 kg and radius 1 m is spinning around its central
axis at a rate of ω = 20 rad/s. A force of magnitude 5 N is applied to the disk. Recall that the
moment of inertia of a solid disk is I=(1/2)mr^2

.
(a) Draw the disk and indicate the direction of rotation. Then draw the direction that the force
should be applied to make the disk stop as quickly as possible.
(b) What is the minimum time needed for the disk to stop?

Homework Equations

$$\tau$$= I$$\alpha$$

$$\tau$$=Fr

The Attempt at a Solution

For part a, I said that the disk was moving counterclockwise, and the fastest way to stop it would be to apply a force that is perpendicular to the radius, because that would produce the largest negative torque. Is that correct?

For part b, I solved for I and got 5 kgm² then I did this:
$$\tau$$=I $$\alpha$$
Fr=5$$\alpha$$
(5N)(1m)=5$$\alpha$$
$$\alpha$$=1rad/²

I then solved for time with the equation:
$$\omega$$f=$$\omega$$i +$$\alpha$$t
0=20rad/s - 1rad/s²(t)
t=20 seconds I don't think this is correct but I'm not sure what else to do. Thank you

 

[gneill]

Looks okay to me!

 

[tiny-tim]

hi pradeepk!

all looks fine

 

[pradeepk]

Thanks Guys!

I just thought that 20 seconds was a very long time to make it stop, but I guess 5 Newtons is a very small force