Question

A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotational axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular acceleration, least to greatest.1. disk, hoop, sphere2. disk, sphere, hoop3. hoop, sphere, disk4. hoop, disk, shpere5. sphere, disk, hoop6. sphere, hoop, disk

Answer 1

Answer:

4 hoop, disk, sphere

Explanation:

Because

We are given data that

Hoop, disk, sphere have Same mass and radius

So let

And Initial angular velocity, = 0

The Force on each be F

And Time = t

Also let

Radius of each = r

So let's find the inertia shall we!!

I1 = m r² /2

= 0.5 mr² the his is for dis

I2 = m r² for hoop

And

Moment of inertia of sphere wiil be

I3 = (2/5) mr²

= 0.4 mr²

So

ωf = ωi + α t

= 0 + ( τ / I ) t

= ( F r / I ) t

So we can see that

ωf is inversely proportional to moment of inertia.

And so we take the

Order of I ( least to greatest ) :

I3 (sphere) , I1 (disk) , I2 (hoop) , ,

Order of ωf: ( least to greatest)

That of omega xf is the reverse of inertial so

hoop, disk, sphere

Option - 4

Answer 2

The ranking of the objects according to their angular acceleration is option 4 hoop, disk, sphere.

Ranking of the objects:

Since

Hoop, disk, sphere contain Same mass and radius

So here

Initial angular velocity, = 0

The Force on each be F

And Time = t

Radius of each = r

Now

I1 = m r² /2

= 0.5 mr² his is for dis

I2 = m r² for hoop

And

Moment of inertia of sphere should be

I3 = (2/5) mr²

= 0.4 mr²

Now

ωf = ωi + α t

= 0 + ( τ / I ) t

= ( F r / I ) t

here,

ωf is inversely proportional to moment of inertia.

Now

Order of I ( least to greatest ) :

I3 (sphere) , I1 (disk) , I2 (hoop) , ,

Order of ωf: ( least to greatest)

That of omega xf is the reverse of inertial so

Therefore, the fourth option is correct.

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