How long for braking force to stop a spinning sphere?

[Kaxa2000]

A solid sphere w/ mass 100kg and radius 1m is spinning on axle. A brake pad is used to slow it down to a stop. While braking a force of 1N is applied on the pad. The coeff. of friction b/t pad and sphere is 0.5. The sphere is initially spinning at 100 rev/s, how long will it take to stop sphere?


Explanation on how to solve will be fine...
I'm guessing you find the moment of inertia of the sphere w/ the equation I = (2/5)MR^2 and then use constant acc techniques to find how long it takes to stop?

 

[Redbelly98]

Explanation on how to solve will be fine...
I'm guessing you find the moment of inertia of the sphere w/ the equation I = (2/5)MR^2 and then use constant acc techniques to find how long it takes to stop?

Yes, if you actually mean constant angular acceleration techniques.

 

[Kaxa2000]

How do I get the third variable?

 

[Redbelly98]

Which two variables do you have already?

You can figure out the angular acceleration from information in the problem statement. Two other variables are given to us directly.

 

[Kaxa2000]

Initial angular velocity = 100 rev/s
Final angular velocity = 0

I don't know how to get the angular acc.

Would you use the torque formula?

tau = Iα ?

I don't know what tau would be

 

[Kaxa2000]

Anyone know?

 

[Redbelly98]

Yes, use tau = I α

You can use the 1N force, and the coef. of friction, here.

 

[Kaxa2000]

I know tau = r x F

would you plug 1N for F? and 1 m(radius of sphere) for r?

tau = 1N x 1m = 1 N m

I = (2/5)(100kg)(1m)^2 = 40 kg m

so
angular acceleration = tau/I = (1/40) rad/s^2

is this right?
How would u use coeff of friction?

 

[ideasrule]

The force that provides torque has to be in the direction opposing the rotation (or else how can the wheel stop?) The 1 N is applied perpendicular to the direction of rotation. How would you use the coefficient of friction to calculate the F in tau=r x F?

 

[Kaxa2000]

Fk = ukN

so the Force would be (0.5)(1N)? = .5 N?

 

[ideasrule]

Yeah, that's right.

 

[Kaxa2000]

I'm getting a negative answer for time? Why is this

I used the

w - w0 = at

formula

 

[Kaxa2000]

Does anyone know why I'm getting a negative t?

t = (w-w0)/(angular acc.)

(0 - 100)/(.0125 rad/s^2) = -8000 s

 

[Redbelly98]

The acceleration is negative in this case, since the sphere's rotation is slowing down and coming to a stop.