1. Torque Calculations with Pulleys

2. Review Newton’s Second Law. Pulley on horizontal surface
Given a mass of 14 kg on a horizontal table. It is attached by a rope over a pulley to a mass of 26 kg which hangs vertically. μ= 0.1 . What is the acceleration?
A = 6 m/s2
FT= 98 N

3. Atwood machine review
Given mass 1 is 90 kg and mass 2 is 50 kg, what is the acceleration?
A = 2.8 m/s2
FT = 630 N

4. Incline Plane with pulley
Given θ = 25 ̊ an incline has a mass of 20 kg placed upon it. It is attached by a rope over a pulley to a mass of 30 kg which hangs vertically. The coefficient of friction is The acceleration will be…
A = 3.5 m/s2
FT = 189 N

5. Pulleys with mass Example Consider a hanging mass wrapped around a
MASSIVE pulley. The hanging mass has
weight, mg, the mass of the pulley is mp, the
radius is R, and the moment of inertia about its
center of mass Icm = 1/2mpR2. (assuming the
pulley is a uniform disk). Determine the
acceleration of the hanging mass.

6. HOW TO: STEPS TO GUIDE THINKING
1. Draw free body diagrams for the masses and the pulley.
2. Write an equation for Net force for each mass’s acceleration.
3. Write an equation for Net Torque for the pulley.
4. In the torque equation, eliminate α and sub a/r.
5. Combine the equations to eliminate T(tension) and be left with unknown a.
6. Solve for a.

7. Ex. 1
A 1.53 kg mass hangs on a rope wrapped around a disk- shaped pulley of mass 7.07 kg and radius 66 cm. What is the linear acceleration of the hanging mass?
A = 2.96 m/s2

8. Ex. 2
A = 2.9 m/s2

9. Ex. 3
A = 7.35 m/s2