A person sits on a frictionless stool that is free to rotate but is initally at rest. The person holding a bicycle wheel (I = 3 kg*m2) that is 8 rev/s in the clockwise direction as viewed from above, and the moment of inertia of the person-sheel-stool system is 9 kg*m2.
1. What is the mignitude of the angular velocity of the PWS?
2. wHAT IS THE MAGNITUDE OF THE ANGULAR MOMENTUMOF THE pws?
The person flips the rotating wheel over 180 degrees.
3. What is the magnitude of the angular acceleration of the person-wheel-stoolsystem?
It should read "person-wheel-stool system"
To answer these questions, we can use the principle of conservation of angular momentum. The total angular momentum of a system remains constant unless an external torque acts on it.
1. To find the magnitude of the angular velocity of the PWS (Person-Wheel-Stool) system, we can use the initial and final moments of inertia and angular velocities. The principle of conservation of angular momentum can be expressed as:
(I1 * ω1) = (I2 * ω2)
Where I1 and I2 are the initial and final moments of inertia, and ω1 and ω2 are the initial and final angular velocities.
We are given:
Initial angular velocity (ω1) = -8 rev/s (in the opposite direction of the clockwise rotation)
Initial moment of inertia (I1) = 9 kg*m^2
Final angular velocity (ω2) = ?
Final moment of inertia (I2) = 9 kg*m^2 (no change in the system)
Solve for ω2:
(I1 * ω1) = (I2 * ω2)
(9 kg*m^2 * -8 rev/s) = (9 kg*m^2 * ω2)
(-72 kg * m^2/ s) = (9 kg*m^2 * ω2)
ω2 = -8 rev/s
The magnitude of the angular velocity of the PWS is 8 rev/s.
2. To find the magnitude of the angular momentum of the PWS, we use the formula:
Angular momentum (L) = moment of inertia (I) * angular velocity (ω)
Given:
Moment of inertia (I) = 3 kg*m^2
Angular velocity (ω) = 8 rev/s
Angular momentum (L) = 3 kg*m^2 * 8 rev/s
L = 24 kg*m^2/s
The magnitude of the angular momentum of the PWS is 24 kg*m^2/s.
3. When the person flips the rotating wheel over 180 degrees, the change in angular momentum is caused by an external torque (the flipping action). We can calculate the angular acceleration by dividing the change in angular momentum by the moment of inertia.
Change in angular momentum = Final angular momentum - Initial angular momentum
Given:
Final moment of inertia (I2) = 9 kg*m^2 (no change)
Initial angular momentum (L1) = 24 kg*m^2/s
Final angular momentum (L2) = ?
Change in angular momentum = L2 - L1
Using the information given, we can solve for L2 by flipping the direction of the initial angular momentum:
L2 = -L1
Change in angular momentum = (-L1) - L1
Change in angular momentum = -2L1
Now, we can calculate the angular acceleration (α):
Change in angular momentum (ΔL) = α * Δt
-2L1 = α * Δt
Dividing both sides by the time (Δt):
α = (-2L1) / Δt
However, the value of Δt (time taken to flip the wheel) is not provided in the given information. Therefore, we cannot determine the magnitude of the angular acceleration without knowing the time taken for the flip.