A ballet dancer spins with 2.4 rev/s with her arms outstretched,when the moment of inertia about axis of rotation is 1 .With her
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a) 6.25 rad/s
The law of conservation of angular momentum states that the angular momentum must be conserved.
The angular momentum is given by:
where
I is the moment of inertia
is the angular speed
Since the angular momentum must be conserved, we can write
where we have
is the initial moment of inertia
is the initial angular speed
is the final moment of inertia
is the final angular speed
Solving for , we find
b) 28.1 J and 35.2 J
The rotational kinetic energy is given by
where
I is the moment of inertia
is the angular speed
Applying the formula, we have:
- Initial kinetic energy:
- Final kinetic energy:
Answer:
The total number of small cylinder = 7.
Explanation:
Lets take
Radius of the large cylinder = R
length = L
L = 10 R
The total area A = 2 π R² + π R L
The length of the small cylinder = l
The number of small cylinder = n
L = n l
The total area of small cylinders
A'=n (2 π R² + π R l)
As we know that emissive power given as
P = A ε σ T⁴
For large cylinder
P = A ε σ T⁴ -----------1
For small cylinders
P'=A' ε σ T⁴ ------2
From 1 and 2
Given that
P'= 2 P
A' ε σ T⁴ =2 A ε σ T⁴
A'=2 A (All others are constant)
n (2 π R² + π R l) =(2 2 π R² + π R L)
n (2 R² + R l) = (2 R² + R L)
L = 10 R
2 n +10 = 2 x 12
2 n +10 = 24
2 n = 24 -10
2 n = 14
n = 7
The total number of small cylinder = 7.