Title: Physics 211 Lec 20: Torque and Angular Momentum
1Physics 211 Lec 20 Torque and Angular Momentum
- Torque - for an application of force at a point
location
Scalar Form
where r ? F
- Vector Form
- Both position and force are vectors
- Rotation due to torque is around an axis
perpendicular to both radius and force
with magnitude ? rFsin? or
? vector moment in direction of rotating axis
The result of a cross product is also a
vector. r position vector from anywhere on axis
of rotation to force location F
force vector
M magnitude of moment r mag of pos vec from
anywhere on axis of rotation to
force ? angle between position vector and force
2The Cross Product a way of multiplying vectors
to a perpendicular result
Think-Pair-Share Task F 0i 6j 2k and r
6i 9j 3k Perform the cross product
calculation for the vector above. Give both the
vector form and its magnitude, the sketch the
vector result
Note Differences between the dot product and
the cross product. Dot Product Cross
Product scalar vector parallel part of vector
multiplication perpendicular part of vector
multiplication
3Torque and Angular Momentum Relationships
Torque Angular Momentum
Diagram
Diagram
Recall Force is derivative of momentum Now
Torque is derivative of angular momentum
4Torque and Ang. Mom Which equation do I use?
Point force or point mass rotating about an axis
Rigid body rotating about an axis
? I? L I?
5Example Ch11 5Wind blowing E exerts 0.785N
horizontal force on flower making its 0.45m long
stem tilt 14 from vertical. Find the vector for
the torque on the flower about its base.
6Example Ch11 17Mass m fired from origin at
speed vi and angle ? with the horizontal. Find
the angular momentum about the origin when it
isa) at the originb) at the peak of its
trajectoryc) about to landd) What torque causes
the changes found above?
7Example Ch11 24Big Ben clock has 2.7m, 60kg
hour hand and 4.5m, 100kg minute hand. Find total
angular momentum of the two hands about the clock
center by treating the hands as uniform thin rods.
8Questions for Groups
- 11.9 Helicopter require at least to rotors for
stable flight. Why? - 11.11 How does the use of a pole help a
tightrope walker balance?