1
Phys141 – Fri 10/21 – Lecture 21
•Today: Chapter 11
•MON: Chapter 12 – Static equilibrium
•Administrative:
Reading for Mon: Chapter 12
Midterm 2: Wed Nov 9
Office hours Mon Nov 7 NOT Wed Nov 9
Final exam Saturday 8am-10am December 17
Torque: tendency of a force to generate
rotation an object about some axis
Torque vector τ= rx F
(vector product)
Direction: perpendicular to
the plane formed by the
position vector and the
force vector (right-hand
rule)
Magnitude: r F sin(θ)
Depends on the choice of point O
Properties of the Vector Product
The order in which the vectors are multiplied is important
Ax B= - Bx A
If Ais parallel to B(θ= 0oor 180o), then Ax B= 0
– For example, Ax A= 0
()
dd d
dt dt dt
×= ×+×
AB
AB BA
A x (B + C) = A x B + A x C
Torque Vector Example
• Example 1: I x j
• Example 2: Given the force
τ= ?
m
N
)
ˆ
00.5
ˆ
00.4(
)
ˆ
00.3
ˆ
00.2(
jir
jiF
+=
+=
ˆˆ ˆˆ
[(4.00 5.00 )N] [(2.00 3.00 )m]
ˆˆ ˆˆ
[(4.00)(2.00) (4.00)(3.00)
ˆˆ ˆˆ
(5.00)(2.00) (5.00)(3.00)
ˆ
2.0 N m
τ
=×= + × +
=×+×
+×+ ×
=⋅
rF i j i j
ii ij
ji ij
k
