A few Angular Momentum and Rotational Kinematics Conceptual Questions

[rustyshackle]

Homework Statement

Each of the questions are either increase, decrease, equal, or undetermined.

1) You are sitting on a rotating chair, holding a 2 kg mass in each arm outstretched. When the masses are dropped, your angular momentum -------.

2) You sit in a rotating chair holding 2 kg masses in each hand close to your chest. When your arms (and masses) are outstretched, the rotational kinetic energy ------.

3) Two equal masses are on a turning wheel at a distance r from the axis of rotation. When the masses are moved to .5r , the angular momentum of the masses ------. Assume no friction.

4) You stand on the edge of a large freely floating platform. As you walk towards the center of the platform, the rate of rotation -------.

5) Two equal masses are on a rotating massless rod at a distance r from the axis of rotation. When the masses are moved to .5r without exerting any external torque, the linear velocity of the masses ---------.

Homework Equations

I = mr^2
I1w1 = I2w2 (conservation angular momentum)
Rotate KE = .5Iw^2
linear v = r*w

The Attempt at a Solution

1) Equal. Conservation of momentum says momentum is conserved, dropping the masses will increase one's angular velocity (w), but the momentum will always be equal without external forces acting.

2) Increases. Rotate KE = .5Iw^2 = .5mr^2w^2, and increasing the value of r would increase the kinetic energy. Does radius actually affect rotational KE since .5Iw^2 reduces to .5mv^2?

3) Equal. Once again, conservation of angular momentum. When r is decrease and m is constant, w will increase to conserve momentum.

4) Increases. Conservation of momentum says mr^2w = mr^2w. If the radius decreases with mass staying constant, w must increase.

5) Increases. Conservation of momentum: mrv (from Iw) = mrv. With constant masses, decreasing r would increase linear velocity.

Thanks

 

[PeterO]

Homework Statement

Each of the questions are either increase, decrease, equal, or undetermined.

1) You are sitting on a rotating chair, holding a 2 kg mass in each arm outstretched. When the masses are dropped, your angular momentum -------.

2) You sit in a rotating chair holding 2 kg masses in each hand close to your chest. When your arms (and masses) are outstretched, the rotational kinetic energy ------.

3) Two equal masses are on a turning wheel at a distance r from the axis of rotation. When the masses are moved to .5r , the angular momentum of the masses ------. Assume no friction.

4) You stand on the edge of a large freely floating platform. As you walk towards the center of the platform, the rate of rotation -------.

5) Two equal masses are on a rotating massless rod at a distance r from the axis of rotation. When the masses are moved to .5r without exerting any external torque, the linear velocity of the masses ---------.

Homework Equations

I = mr^2
I1w1 = I2w2 (conservation angular momentum)
Rotate KE = .5Iw^2
linear v = r*w

The Attempt at a Solution

1) Equal. Conservation of momentum says momentum is conserved, dropping the masses will increase one's angular velocity (w), but the momentum will always be equal without external forces acting.

Love the first word. Love the next 7 words. Don't like the rest.
In the initial situation, You had some angular momentum, and the masses had some angular momentum.
When you released the masses, their part of the initial angular momentum goes with them, causing them to do what ever they do, while your angular momentum remains with you. The important thing is that your rate of rotation will not change, since neither your mass nor your angular momentum changed.

I have not read the rest of your answers yet.

2) Increases. Rotate KE = .5Iw^2 = .5mr^2w^2, and increasing the value of r would increase the kinetic energy. Does radius actually affect rotational KE since .5Iw^2 reduces to .5mv^2?



3) Equal. Once again, conservation of angular momentum. When r is decrease and m is constant, w will increase to conserve momentum.

4) Increases. Conservation of momentum says mr^2w = mr^2w. If the radius decreases with mass staying constant, w must increase.

5) Increases. Conservation of momentum: mrv (from Iw) = mrv. With constant masses, decreasing r would increase linear velocity.

Thanks

comment on 1 included above.