Question

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.

Answer 1

Answer:

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

$KE=\dfrac{1}{2}I\omega ^2$

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

$\dfrac{KE_1}{KE_2}=\dfrac{I_1}{I_2}$

$\dfrac{KE_1}{KE_2}=\dfrac{mr^2}{0.5mr^2}$

$\dfrac{KE_1}{KE_2}=2$

KE₁= 2 KE₂

Therefore answer is C.