Atwood Machine with Massive Pulley

1
Atwood Machine with Massive Pulley
Pulley with moment of inertia I, radius R. Given
M1, M2, and H, what is the speed of M1 just
before it hits the ground?
Strategy Use conservation of mechanical energy.

1. Write down initial kinetic and potential energy.
2. Write down final kinetic and potential energy.
3. Set them equal (no friction).

Three steps
Initial kinetic energy is 0. Initial potential
energy is M1gH. Final kinetic energy is
translational energy of both blocks plus
rotational energy of pulley. Final potential
energy is M2gH. Set final energy equal to initial
energy.
HINT
2
Static balance and a strange yo-yo.
The mass M of the yo-yo is known. The ratio of r
and R is known. What is the tension T1 and T2,
and mass m?
Strategy

1. Write down torque equation for yo-yo.
2. Write down force equation for yo-yo and mass m.
3. Eliminate unknowns.

3
The case of the strange yo-yo.
M is known, R/r is known.
Equations to solve
Torque
Force on mass m.
Mg
Force on yo-yo.
Step 1 Rearrange.
Step 2 Substitute.
Step 3 Solve (aR/r).