Copyright © 2012 Pearson Education Inc. Rotation Physics 7C lecture 10 Thursday October 31, 8:00 AM...
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Transcript of Copyright © 2012 Pearson Education Inc. Rotation Physics 7C lecture 10 Thursday October 31, 8:00 AM...
Copyright © 2012 Pearson Education Inc.
Rotation
Physics 7C lecture 10
Thursday October 31, 8:00 AM – 9:20 AMEngineering Hall 1200
Copyright © 2012 Pearson Education Inc.
External forces and center-of-mass motion
• When a body or collection of particles is acted upon by external forces, the center of mass moves as though all the mass were concentrated there.
Copyright © 2012 Pearson Education Inc.
External forces and center-of-mass motion
• Fragments of a firework shell would fly at 100 m/s for 5 seconds before they burn out. If a shell reaches its max height of 1000 meter and explodes, are the audiences on the ground safe from burning fragments? Ignore air resistance.
Copyright © 2012 Pearson Education Inc.
External forces and center-of-mass motion
• Fragments of a firework shell would fly at 100 m/s for 5 seconds before they burn out. If a shell reaches its max height of 1000 meter and explodes, are the audiences on the ground safe from burning fragments? Ignore air resistance.
motion of center of mass:
motion of fragments relative to center of mass:
Copyright © 2012 Pearson Education Inc.
Rocket propulsion
• As a rocket burns fuel, its mass decreases, as shown in Figure below.
• What is the speed of rocket if we know the exhaust speed vex, burning rate λ=dm/dt and initial mass m0?
Copyright © 2012 Pearson Education Inc.
Rocket propulsion
between time t and t + dt, according to momentum conservation:
(m+dm) v = m (v+dv) + dm (v-vex)
• What is the speed of rocket if we know the exhaust speed vex, burning rate λ=dm/dt and initial mass m0?
Copyright © 2012 Pearson Education Inc.
Rocket propulsion
between time t and t + dt, according to momentum conservation: (m+dm) v = m (v+dv) + dm (v-vex)
m dv – v dm + (v-vex) dm = 0
(m0- λ t) dv –vex λ dt = 0
dv - λ vex dt /(m0- λ t)= 0
v + vex ln(m0- λ t) = constant
v = v0 + vex ln (m0/(m0- λ t)) = v0 + vex ln (m0/m)
• What is the speed of rocket if we know the exhaust speed vex, burning rate λ=dm/dt and initial mass m0?
Copyright © 2012 Pearson Education Inc.
Introduction
• The north star is Polaris today, but 5000 years ago it was Thuban. What caused the change?
• What causes bodies to start or stop spinning?
• We’ll introduce some new concepts, such as torque and angular momentum, to deepen our understanding of rotational motion.
Copyright © 2012 Pearson Education Inc.
Introduction
• How do we quantify the spinning of wind turbine?
Copyright © 2012 Pearson Education Inc.
Angular displacement
• angular displacement: θ
• unit: radian
• direction: (right hand rule!)
Copyright © 2012 Pearson Education Inc.
Angular displacement and velocity
• How do we quantify the spinning of wind turbine?
ω = dθ /dt
Copyright © 2012 Pearson Education Inc.
Angular velocity is a vector!
• signs of angular displacement
Copyright © 2012 Pearson Education Inc.
Right hand rule
• Angular displacement is a vector, use right hand rule to determine the direction.
Copyright © 2012 Pearson Education Inc.
These are very similar to linear motion
• linear and angular motion:
Copyright © 2012 Pearson Education Inc.
Example
• calculate the acceleration of the black point in the disk.
Copyright © 2012 Pearson Education Inc.
Example
• calculate the acceleration of the black point in the disk.
Copyright © 2012 Pearson Education Inc.
Example
• calculate the acceleration of the black point in the disk.
Copyright © 2012 Pearson Education Inc.
Speed of propeller
• calculate the speed of the tip of the propeller.