Two wheels having the same radius and mass rotate at the same angular velocity. one wheel is made with spokes so nearly all the mass is at the rim. the other is a solid disk. how do their rotational kinetic energies compare?

a. the wheel with spokes has higher ke, but not twice as high.
b. the solid wheel has higher ke, but not twice as high.
c. the wheel with spokes has about twice the ke.
d. the solid wheel has about twice the ke.
e. they are nearly the same.

C. The wheel with spokes has about twice the KE.

Explanation:

Given that

Mass , radius and the angular speed for both the wheels are same.

radius = r

Mass = m

Angular speed = ω

The angular kinetic energy KE given as

I=Moment of inertia for wheels

Wheel made of spokes

I₁ = m r²

Wheel like a disk

I₂ = 0.5 m r²

Now by comparing kinetic energy

KE₁= 2 KE₂

Therefore answer is C.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

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