# Rotational motion, Pulley system

1. Apr 26, 2010

### zames99

1. The problem statement, all variables and given/known data
A 5kg mass and a 10kg mass are connected by a rope and hung over a pulley. The pulley is a disc with a mass of 5kg and a radius of 10cm. the two masses are initially at rest with the 10kg mass 50cm higher than the 5kg mass.
Find, The speed of each mass at the instant they pass one another
The torque exerted on the pulley by the masses
The angular momentum of the pulley at the instant the masses pass one another.

2. Relevant equations
L = m(r * v)
T = r * F
I(disc) = 1/2 mv^2

3. The attempt at a solution
Part (1)
F=(10-5)*9.8 = 49N
Mtotal = (10+5)=15
a =49/15 =3.26 ms^-2
v^2 = 0^2 + 2 * 0.5 * 3.26
v = 1.8 m/s

Part (2)
The only external forces acting on the disc are m1*g and m2*g
T = r * F
T = r (m2*g-m1*g)
T = 0.1 (10*9.8-5*9.8)
T = 4.9 Nm
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 26, 2010

### Filip Larsen

Your answer to part 1 does not look correct. Assuming no frictional losses, you may find it helpful to equated the mechanical energy (i.e. the sum of potential and kinetic energy) of the three masses before they are released with the mechanical energy of the system when the two masses pass each other. Doing that, you should arrive at a speed around 1.11 m/s.