Transcript rotational inertia

Circular Motion
Rotation and Revolution

When a body turns about it’s axis is
known as a rotation.
– A skater spins about their axis.
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When a body turns about an external axis
is known as a revolution.
– A Merry Go Round rotates while the riders on
the ride revolve around the Merry Go Round.
Rotational Speed
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Tangential Speed
– Speed of a point around the circumference of a
circular path.
 Speed varies according to the distance from the axis.
– Points farther away from the axis have a higher tangential
velocity than points closer the axis because they have a larger
distance to cover.
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Angular speed
– Number of rotations in a given amount of time.
 Rotations per minute.
 All points on a rigid circular object have the same angular
speed.
Centripetal Force

Any force that causes an object to follow a
circular path.
– Types of Centripetal Forces
 Gravity – Keep Satellites in orbit.
 Tension – Pull on a string keeps a ball in a circular path.
 Friction – The tires experience and inward force of friction to
keep a car from skidding sideways around a turn.
 Normal Force – The supporting force of a car door when a
car travels around a sharp curve.
– Without centripetal forces the objects would continue
to move straight ahead tangent to the circular path.
Without a centripetal force the
object continues on a straight path.
Center of Gravity
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Point in which most of the weight is centered in an
object.
– Sometimes called the center of mass.
– For a symmetrical object the center of gravity is its geometric
center.
– For irregular shaped objects its where most of the mass is
concentrated.
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An object tends to rotate around the center of gravity as
if it were a stationary point.
– It is the balance point that supports the entire object.
– The center of gravity can also exhist where there is no material
at all. For example a hollow sphere has the center of gravity at
its geometric center.
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A ball will tend to roll so that its center of gravity is as
low as possible to the ground.
Toppling and Center of Gravity
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If the center of gravity is above the area
of support the object will remain upright.
– The leaning tower of Pisa does not topple
because the center if gravity does not extend
beyond is support base.
Rotational Mechanics
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Torque
– Force applied to an object that makes it
rotate.
– Torque is produced when a force is applied
with leverage.
 The longer the handle the more leverage.
 The force must be applied perpendicular to the
pivoting point.
 The lever arm is the distance between the pivot
point and the force applied.
– Torque = length of lever arm x force (perpendicular)
Balanced Torques
A balanced teeter totter represents
balanced torques because the clockwise
rotation equals the counterclockwise
rotation.
 Torque and center of gravity. If you stand
with your back to the wall and try to touch
your toes you will rotate.
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– Your center of mass is not over your base so
you topple over.
Rotational Inertia
An object rotating about its axis will continue to
rotate about its axis.
 The resistance to a change in rotation is called
rotational inertia sometimes called moment of
inertia.
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– Torque is required to change the rotational inertia of
an object.
– Depends on the distribution of mass.
– Greater distribution of mass more roatational inertia.
 In other words if the mass is distributed around the edges of
the object it is more difficult to rotate.
Angular Momentum
Angular momentum is product of
rotational velocity and rotationla inertia.
 Angular momentum is a vector that acts
along the axis of rotation.
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