1. Aim: How do we explain angular momentum?

2. Vector Nature of Rotation
Recall definition of cross product: a x b = ? a x b is a vector perpendicular to the plane defined By vectors a and b

3. Torque
Torque is the cross product of force and the radial vector r. τ=r x F

4. Angular Momentum
A rigid body can rotate. If its center of mass does not move it has no linear momentum. However, the other particles in the rigid body move in a circle. Thus, the momentum associated with the rotation of the rigid body is called angular momentum

5. Defining angular momentum
L=mvrsinθ L= angular momentum of an object relative to the origin m=mass of an object v=velocity of the object r=displacement of object with respect to the origin θ=angle between r and v

6. Angular momentum
Angular momentum is the cross product of r and linear momentum p. (Linear momentum p = mv)

7. Other Expressions for Angular Momentum
L = Iω L= angular momentum of object about a reference point I= moment of inertia about an axis through the reference point ω=angular speed with respect to axis

8. Is rotation necessary for angular momentum?

9. Angular Momentum Problem 1
A car of mass 1,500 kg moves on a circular race track of radius 50 m with a speed of 40 m/s. What is the magnitude of its angular momentum relative to the center of the track? L=mvrsinᶿ=1500(4)(50)sin90=3,000,000 kg m2/s
3 x 10^6 kg m^2/s

10. Thought Question 1
Rank the points according to the angular momentum of the particle measured about them, greatest first.
b,c=d,a=e

11. Angular Momentum Problem 2
What is the angular momentum of the Earth due to its
revolution about the Sun, relative to the Sun
rotation about its axis, relative to the axis?
a) 2.7 x 10^40 kg m^2/s b) 7.1 x 10^33 kg m^2/s

13. Angular Momentum Problem 3
The position vector of a particle of mass 2.00 kg is given as a function of time by r = (6.00ti +5.00tj) m. Determine the angular momentum of the particle about the origin, as a function of time. v(t)=6i +5j L=mvr= (2)(6i+5j)(6ti+5tj)= (72ti + 50tj)kg m2/s

14. Angular Momentum Problem 4
A particle of mass kg is attached to the 100 cm mark of a meter stick of mass kg. The meter stick rotates on a horizontal frictionless table with an angular speed of 4 rad/s. Calculate the angular momentum of the system when the stick is pivoted about an axis a) perpendicular to the table through the 50 cm mark b) perpendicular to the table through the 0 cm mark
a) b) 1.73