Wheels A and B in Figure 1 are connected by a belt that does not slip. The radiu
ID: 1458515 • Letter: W
Question
Wheels A and B in Figure 1 are connected by a belt that does not slip. The radius of wheel B is three times the radius of wheel A. What would be the ratio of the rotational inertias IA/IB if the two wheels had (a) the same angular momentum about their central axis and (b) the same rotational kinetic energy?
Wheels A and B in Figure 1 are connected by a belt that does not slip. The radius of wheel B is three times the radius of wheel A. What would be the ratio of the rotational inertias IA/IB if the two wheels had (a) the same angular momentum about their central axis and (b) the same rotational kinetic energy?Explanation / Answer
Let us consdier
The mass of the wheel A =m1
The mass of the wheel B =m2
Given that radius of A =R
Radius of B =3R
a)
Since both the wheels are joined to the same belt then the system has the same linear velocity
VA =VB
we know that v =rw then
wARA =wBRB
wA/wB =3R/R
wA/wB =3-------(1)
Now from the conservation of angular momentum
LA =LB
IAwA =IBwB
IA/IB =wB/wA =(1/3) from equation (1)
Now from the conservation of energy
KEA =KEB
(1/2)IAwA2 =(1/2)IBwB2
IA/IB =(wB/wA)2
IA/IB =(1/3)2
IA/IB =1/9
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.