Name: _________________________
Recitation 10 Quiz
A uniform solid cylinder of mass m1 and radius R is mounted on frictionless bearings about a fixed axis
through O. The moment of inertia of the cylinder about the axis is I = ½m1R2. A block of mass m2,
suspended by a cord wrapped around the cylinder as shown above, is released at time t = 0.
a.
On the diagram below draw and identify all of the forces acting on the cylinder and on the block.
b.
In terms of ml, m2, R. and g, determine each of the following.
i.
The acceleration of the block.
ii.
The tension in the cord.
iii. The angular speed of the disk as a function of time, t.
iv. The angular speed of the disk as a function of distance fallen, h.
Per: _____
Recitation 10 Quiz RUBRIC
(a)
4 points
(b)
i. and ii. 6 points total
For using Newton’s 2nd Law with two forces acting on the block
1 pt
m2a = m2g-T
For using Newton;s 2nd Law with torques for the pulley:
1 pt
For expressing the torque about the pulley in terms of the tension
1 pt
For relating the linear acceleration to the rotational acceleration
1 pt
I =
 = RT
a = R
Substitute the tension expression in one equation into the other
T = m2g-m2a
½ m1R2 = R(m2g-m2a)
For correct answers for the tension and the acceleration
a
m2 g
m2  12 m1
1 pt
T
m2 m1 g
2m2  m1
1 pt
iii. 2 points
For expressing the angular speed using a constant rotational acceleration relationship
1 pt
For substituting the linear acceleration from part (b) i to express the rotational acceleration
1 pt
  t

m2 g
R ( m2 m1 )

m2 g
R ( m2  m1 )
t
iv. 3 points
For using conservation of energy with kinetic energy for both the mass and pulley
m2gh = ½ m22 + ½ I2
For relating linear speed of mass to rotational speed of pulley
=R
For the correct answer

2m2 gh
1
1
2 m2  4 m1
1 pt
1 pt
1 pt