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Rotational Motion

Uniform Circular Motion
The object’s speed is constant but its
direction is changing.
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Important to driving (how fast can I take a
curve on the road?) and satellites in orbit
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Rotational Motion
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Period
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The time to return to the original position.
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Rotational Motion

Centripetal Acceleration
The acceleration of an object moving along a
circular path.
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v
ac
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Rotational Motion

Newton’s 2nd Law and Centripetal Acceleration
What is the force that causes an object to accelerate
in a circle?
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• Tension, gravity, friction, etc.
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Rotational Motion

Artificial Gravity
Rotation causes the normal force which is assumed
to be the force of gravity.
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Training for astronauts
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Missions to Mars and beyond
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Rotational Motion

Torque (τ )
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A force that causes or opposes rotation
Depends on the net force applied and the
distance of the net force from the axis of rotation.
τ = Fnet r
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ccw
is + and cw
is -
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Rotational Motion

Moment of Inertia ( I )
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The resistance to change in angular motion
τnet = I α
Similar to Newton’s 2nd Law: Fnet = m a
I depends on the mass of an object’s particles
and their distance from the axis of rotation
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Rotational Motion

Angular Momentum ( L )
Similar to linear momentum but includes the
distance from the axis of rotation
L = (mv) r
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m
r
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v
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Rotational Motion

Torque and Angular Momentum
A net torque applied during a time interval will
change an object’s angular momentum
τnet Δt = ΔL
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Example: riding a bicycle
• Stability – bicycles, footballs, gyroscopes
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Rotational Motion

Conservation of Angular Momentum
If no net, external torque is applied to an object,
its angular momentum is constant.
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• The moment of inertia and the angular velocity will
increase or decrease
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Examples: skaters, gymnasts, divers, helicopters
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