1. Torque and Moments of Inertia
Physics 111
Torque and Moments of Inertia

2. Equations: Torque (t) = F * L T=F * d sin ɵ If not rotation-
Delta Fy: 0
Delta Fx: 0
Torque : 0
For uniform distribution of mass
Weight .5 L
Summation of t = I ᾰ
I = Summation of mr^2

3. Problem 1 -
The pull cord of a lawnmower engine is wound around a drum of radius 6 00 cm while the cord is pulled with a force of 75.0 N to start the engine. What magnitude torque does the cord apply to the drum?

4. Solution:
T = r*f
(.06 * 75) = 4.5 N * m

5. Practice Problem 2:
Revolutionaries attempt to pull down a statue of the Great Revolutionaries attempt to pull down a statue of the Great Leader by pulling on a rope tied to the top of his head. The statue is 17 m tall, and they pull with a force of 4200 N at an angle of 65° to the horizontal.
What is the torque they exert on the statue?
If they are standing to the right of the statue, is the torque positive or negative?

6. Solution: Given: height= 17m F = 4200 Angle = 65 Find: torque
First find the length between the axis of rotation and the line of action
sin(65) = 17 m / L
L = 17 m / sin 45 = 20 m
T = l * F = 20 * = N. m
Is positive, so moving ccw

7. Practice Problem:
What is the rotational inertia of a solid iron disk of mass 49 0 kg with a thickness of 5 00 cm solid iron disk of mass and a radius of cm, about an axis through its center and perpendicular to it?
Need to use moments of inertia of common shapes table!

8. Solution: For disk I = .5 mr^2 Need to convert cm to meters.
I = .5 ( 49)(.2)^2 = .98 kg * m^2

9. Problem:
Find the moment of inertia of the system below. The masses are m1 an d m 2 and they are separated by a distance r. Assume the rod connecting the masses is massless. ( moving ccw)
Take m1 = 2.00 kg, m2 = 1.00 kg, r1= m , and r2 = 0.67 m. M2 M1

10. I = summation of mr^2 I = m1r1^2 + m2r2^2
Solution:
I = summation of mr^2
I = m1r1^2 + m2r2^2
= (2 kg)(.33m)^2 + (1 kg)(.67m)^2
= .67 kg m^2

11. Part 2 :
What is the moment of inertia if the axis is moved so that is passes through m1?
What does this mean?

12. Solution Part 2: I = summation of mr^2 I = m1r1^2 + m2r2^2
= (2 kg)(0)^2 + (1 kg)(1 m)^2
= 1 kg m^2
Moment of Inertia increased!