Answer:
(a) 110 rev/ min
(b) 5/6
Explanation:
As per the conservation of linear momentum,
L ( initial ) = L ( final )
I' ω' = ( I' + I'' ) ωf
I' is the rotational inertia of first wheel and I'' is the rotational inertia of second wheel which is at rest.
(a)
So, ωf = I' ω' / ( I' + I'' )
As I'' = 5I'
ωf = I' ω' / ( I' + 5I' )
ωf = ω'/ 6
now we know ω' = 660 rev / min
therefore ωf = 660/6
= 110 rev/ min
(b)
Initial kinetic energy will be K'
K' = I'ω'² / 2
and final K.E. will be K'' = ( I' + I'' )ωf² / 2
K'' = ( I' + 5I' ) (ω'/ 6)²/ 2
K'' = 6I' ω'²/72
K'' = I' ω'²/ 12
therefore the fraction lost is
ΔK/K' = ( K' - K'' ) / K'
= {( I'ω'² / 2) - (I' ω'²/ 12)} / ( I'ω'² / 2)
= 5/6
Answer:
22J
Explanation:
Given :
radius 'r'= 3cm
rotational inertia 'I'=4.5 x
kgm²
mass on one side of rope '
'= 2kg
mass on other side of rope'
' =4kg
velocity'v' of mass
' = 2m/s
Angular velocity of the pulley is given by
ω = v /r => 2/ 3x 
ω = 66.67 rad/s
For the rotating body, we have
KE =
I ω²

= 10J
Next is to calculate kinetic energy of the blocks :

=12J
Therefore, the total kinetic energy will be
KE =
=10 + 12
KE= 22J
Circumference of the tire = (2 pi) x (radius)
= (2 pi) x (0.62 meter)
= 3.9 meters
If the tire never slips or skids, then the speed of the vehicle is
speed = (distance) / (time to cover the distance)
= (5 x 3.9 meters) / 1 second
= 19.48 meters/second .
(about 43.6 miles per hour) .
We can't say anything about the vehicle's velocity, because we have
no information about the direction in which it's heading.
Answer:
α=0.625rad/s^2
v=340m/s
w=10rad/s
θ=320rad
Explanation:
Constant angular acceleration = ∆w/∆t
angular acceleration = 20/32
α=0.625rad/s^2
Linear velocity v=wr
v = 20×17= 340m/s
Average angular velocity
w0+w1/2
w= 0+20/2
w= 20/2
w=10rad/s
What angle did it rotate with
θ=wt
θ= 10×32
=320rad