Final answer:
When the radius of the circle in which a block revolves is shortened, the block's angular speed increases to conserve angular momentum. Using the conservation of angular momentum formula, the new angular speed of the block is calculated to be 11.56 rad/s.
Step-by-step explanation:
The subject of this question is Physics, specifically related to the concept of conservation of angular momentum. In this scenario, when the cord is pulled to shorten the radius of the circle in which the block revolves, the angular speed of the block increases to conserve the angular momentum, since the system is frictionless and isolated.
To calculate the new angular speed after the radius is shortened, we can use the conservation of angular momentum:
L_initial = L_final
Where:
m = mass of the block
v = linear speed of the block
r = radius of the circle
ω = angular speed of the block
The angular momentum L for a point mass in circular motion is given by L = mvr = mωr^2. Hence, mω_initial r_initial^2 = mω_final r_final^2. Plugging in the given values:
2.50×10^{-2} kg × 2.89 rad/s × (0.300 m)^2 = 2.50×10^{-2} kg × ω_final × (0.150 m)^2
Solving for ω_final yields:
ω_final = (2.89 rad/s × (0.300 m)^2) / (0.150 m)^2
ω_final = 2.89 rad/s × (2)^2 = 2.89 rad/s × 4 = 11.56 rad/s
Therefore, the new angular speed is 11.56 rad/s.