# Calculating Moment of Inertia of Sphere w/ Mass 100kg & Radius 1m

• Kaxa2000
In summary: The negative sign indicates that the angular velocity is decreasing. In summary, a solid sphere with a mass of 100kg and radius of 1m is spinning on an axle. To stop the sphere, a brake pad applies a force of 1N with a coefficient of friction of 0.5. The initial angular velocity of the sphere is 100 rev/s and the final angular velocity is 0. Using the torque formula and the given variables, the angular acceleration is calculated to be -0.0125 rad/s^2. The time it takes for the sphere to stop can be found using the formula t = (w-w0)/alpha, which results in a negative value of -8000 seconds due to the decrease in angular
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?

Kaxa2000 said:
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.

How do I get the third variable?

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.

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

Last edited:
Anyone know?

Yes, use tau = I α

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

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?

Last edited:
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?

Fk = ukN

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

Yeah, that's right.

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

I used the

w - w0 = at

formula

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

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

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

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

Last edited:

## 1. What is the formula for calculating moment of inertia of a sphere?

The formula for calculating moment of inertia of a sphere is I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius of the sphere.

## 2. How do I calculate the moment of inertia of a sphere with a mass of 100kg and a radius of 1m?

In this case, the moment of inertia would be: I = (2/5) * 100kg * (1m)^2 = 40kgm^2.

## 3. What are the units for moment of inertia?

The units for moment of inertia are kilogram-meter squared (kgm^2).

## 4. What is the significance of calculating moment of inertia for a sphere?

Calculating moment of inertia for a sphere helps in understanding its rotational motion and its resistance to changes in rotational motion.

## 5. Can moment of inertia be negative?

No, moment of inertia cannot be negative as it represents the distribution of mass around an axis and cannot have a negative value. It can, however, be zero if the mass is concentrated at the axis of rotation.

Replies
40
Views
3K
Replies
16
Views
3K
Replies
2
Views
7K
Replies
2
Views
4K
Replies
1
Views
746
Replies
24
Views
3K
Replies
6
Views
1K
Replies
2
Views
1K
Replies
3
Views
2K
Replies
4
Views
6K