1. F1 F2
If F1 = F2…
…no change in motion
(by Newton’s 1st Law)

2. However… F1 F2 If F1 = F2 under this condition… …the block will twist
So the location of the forces is important

3. Torque…
…is the rotational form of the word Force.
Think of it as a twisting Force
Torque equals the amount of force multiplied by its perpendicular distance away from the axis of rotation.
Τ = r x F

5. F1 Fg
Suppose F1 = 100 N. The Fridge is 3m tall and 1 m wide. It is just about to tip. What is the weight of the fridge?

7. A light cable is wrapped around a large solid cylinder several times
A light cable is wrapped around a large solid cylinder several times. When the cable is pulled out with a constant force, the cylinder spins without slipping. It starts from rest.
ω2 = ? F
M = 50 kg
R = 0.7 m
x = 6 m
F = 100 N
α = ?
a = ?

8. Campbell - Physics Notes
solid cylinder
Campbell - Physics Notes
Find the acceleration of the block and the tension in the string
8/31/2018 M r
M = 6 kg
m = 2 kg m

9. solid cylinder
Find the acceleration of the yo-yo and the tension in the string
m = 2 kg m r

10. Campbell - Physics Notes
solid cylinder
Find the velocity of the yo-yo after it has fallen 0.5 m. (starting from rest)
8/31/2018
m = 2 kg m r

11. solid cylinder
Find the acceleration of the cylinder and the friction on the ramp
m = 3 kg
 = 30 m r 

12. Pulley is a Thin-Shell cylinder w/ mass and radius
Table is frictionless.
Given: m1 m2 m3 r
=3 kg
=2 kg
=0.5 kg
= 0.25 m
a1 = a2 = 3.6 m/s2
α = 14.3 rad/s2 a1
T1=? m3 m1 α r
T2=? m2 a2
Calculate:
a1= a2=
α =
T1= T2=
Free Body Diagrams
T1= 10.7 N T2= 12.5 N

14. P = P’ (mv)a + (mv)b = (mv)’a + (mv)’b
Conservation of Angular Momentum
P = P’
(mv)a + (mv)b
= (mv)’a + (mv)’b

15. Campbell - Physics Notes
solid cylinder
A child stands on the edge of a small merry-go-round that is rotating at a rate of 2 rad/s. If the child walks in toward the center of the “disk” and stops 0.5 m for the center, what will happen to ω of the merry-go-round?
8/31/2018
M =100kg
m = 30kg
R = 2.5 m
r = 0.5 m M R r

16. Angular Momentum
P = mv
P = mv
= F.t
…so P =
F.t
And P = F t

17. Front view Angled view Side view Identify: Direction of ω
Direction of L
Direction of Torque
Same
Perpendicular to L
…Use Right Hand Rule RHR’s

18. Campbell - Physics Notes
Angled view
8/31/2018
Side view

19. Angled view
Side view

21. Free Body Diagrams m1 m2 T1 a T1 T2 T1 = m1a  = (T2 r) – (T1 r) = Iα
r(T2– T1)= (m3r2)(a/r)
substitute T2
T2– T1 = m3a m2 a
m2g – m2a -
m1a
= m3a
m2g
m2g – T2 = m2a
Solve for “a”…
substitute
m2g – m2a = T2