Rotational Vectors and Angular Momentum
Angular Velocity• Angular velocity is a vector and its
direction is perpendicular to the plane of rotation.
• Right-hand Rule: Curl your fingers in the direction of rotation, then the thumb points in the direction of angular velocity.
• Counter-clockwise rotation - Positive
• Clockwise rotation - Negative
Angular Acceleration
• What is the average angular acceleration for a top when the angular velocity goes from
to in 0.5s?
dt
d
sradki / ˆ16ˆ4 sradkj / ˆ16ˆ4 z
x
y
z
x
y
Torque• Magnitude -
• Direction - Use the right hand rule.
• Mathematically -
• Matrix Method - Find the determinant of the following matrix.
sinrF
Fr
zyx
zyx
FFF
rrr
kji ˆˆˆ
Torque Example• What is the torque exerted about the origin
by a force if it is applied at the point ?
Nki ˆ3ˆ5 mkj ˆ2ˆ4
Angular Momentum
• For a particle, angular momentum is calculated by the formula
• Ex. What is the angular momentum of the Halley’s Comet at perihelion?
prL
mr 101079.8 smv /106.54 3
kgm 5100.3
What happens to Halley’sComet as it swings awayfrom the sun?
Conservation of Angular Momentum
• In terms of angular velocity
• Analogous rotational Newton’s 2nd Law
IL
dt
Ld
• Conservation of Angular Momentum– If there is no net external torque on a system,
then the angular momentum is constant.
Merry-Go-Round• A merry-go-round is similar to a circular
disk with a mass of 100kg and a radius of 2.0m. It is rotating at 1.57 rad/s when a stationary man of mass 70kg jumps on the edge. What is the new angular velocity?
• The man now moves to within 1.0m of the center. Now what is the angular velocity
Conservation of Angular Momentum
• Orientation of earth is maintained
• Plane of earth’s orbit is maintained.
• Ex. Gyroscope
Eq.
N.P.
Sun
S.P.
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