Item 5 A wheel is turning about an axis through its center with constant angular

Question

Item 5

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t=0, the wheel turns through 7.50 revolutions in t= 15.0 s . At 15.0 s the kinetic energy of the wheel is 33.0 J .

Part A

For an axis through its center, what is the moment of inertia of the wheel?

Express your answer with the appropriate units.

Item 5

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t=0, the wheel turns through 7.50 revolutions in t= 15.0 s . At 15.0 s the kinetic energy of the wheel is 33.0 J .

Part A

For an axis through its center, what is the moment of inertia of the wheel?

Express your answer with the appropriate units.

Explanation / Answer

Solution:

As we know;

= (1/2)t2 and 7.5 revolutions = 7.5 x 2 = 47.14 rad

=> 47.14 =  (1/2) 152

=> = 0.419 rad/s2

and

w= t => w =0.419×15

=> w = 6.285 rad/s

and as we know;

K.E = (1/2)×I×w2

=> 33 = (1/2)×I×(6.285)2

=> I = 1.67 kg-m2

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