Rotational Motion and Torque
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Transcript Rotational Motion and Torque
Chapter 7 and 8
Physics
- When an object spins it is said to undergo
rotational motion. (motion of a body as it
spins around an axis of rotation)
- Axis of rotation – a fixed point, around
which something turns, perpendicular to
the rotation
- Objects can rotate in multiple directions
(dimensions) at the same time (x, y, and
z), which
would give
them multiple
axes of
rotation
relative to
each
dimension.
- Rotational motion is described
in terms of the angle through
which a point moves around the circle.
r = radius from axis of rotation (measured in meters)
s = arc length through which
motion occurs
(measured in meters)
θ = angle through which rotation occurs
(measured in radians)
- Angles measured in radians
360o = 2
radians ------- 1 radian is
approximately 57.3o
1 radian =
57.2957 degrees
1 degree =
0.0174532 radians
- Angular
displacement the angle
through which
a point, line, or
body is rotated
in a specific
direction and
around a
specific axis
Describes how much the object has rotated
Δθ = Δs
r
Angular displacement = change in arc length
distance from axis of rotation
• The change in arc length is considered
positive if the rotation is in the counterclockwise direction, and negative if the
rotation is in the clockwise direction.
- Angular speed (ω)– the rate at which a body
rotates about an axis (radians per second)
Describes the rate of rotation
Measured in:
radians per second
-ORrevolutions per
unit of time
ωavg = Δθ
Δt
Average angular speed = Angular displacement
Time interval
ωavg = measured in radians / second
Δθ = measured in radians
Δt = measured in seconds
• Angular acceleration – the rate of change of
angular speed (radians / s2)
Symbolized by the Greek letter α (alpha)
*All points on a rotating rigid object have the same
angular acceleration and the same angular
speed as all other points on the object.
If this were not true, then the object would
change shape as the object rotated.
• Linear and Angular quantities correspond
to each other. They are like twins in a
different reality.
Centripetal and Tangential
Tangential speed – the linear speed of an
object directed along the tangent to the
object’s circular path.
*If the object were to shoot straight off of
the spin, it would go in a straight line at the
tangential speed.
Tangential acceleration – the
instantaneous linear acceleration of an
object directed along the tangent to the
object’s circular path.
*A measure of the acceleration of an object
over a short interval, in a linear direction
as the object is speeding up or slowing
down, moving in a circle.
Centripetal acceleration – acceleration
directed toward the center of a circular
path
Causes of Circular Motion
• As an object spins around
fixed axis, there is “force” that
pushes the ball outward and
tries to keep it moving out in
a straight line, but there is
also a force that pulls the
object continually back
toward the center of the
rotation.
• Inertia is the “force” that makes the object
move outward from the rotation axis,
which tries to make the object move in a
tangent to the circle around which the
object rotates. The farther from the center
of rotation, the more the inertia tries to
keep the object moving outward.
• When objects are not rigidly attached to
the rotational axis, an outside force must
push / pull on the object to keep it
spinning. Gravity is such a force that acts
on the mass of an object by the mutual
attraction between two objects due to the
mass of each object and the distance
between them.
• Without this “retaining force” the object
would spin off into the air or space.
Satellites in Orbit
• Satellites are objects which orbit another body.
Considered projectiles
Examples: Moon, Space Station,
TV station satellite
• Gravity between the Earth and the Moon is
just enough to counteract the velocity of
the Moon trying to spin off into space on a
tangential trajectory.
• If the
tangential
speed of the
object is high
enough to
overcome
gravity, the
satellite will
escape
Earth’s
gravitational
pull.
• If the tangential speed of the object is not
high enough to just counteract the Earth’s
pull, then the satellite will crash down on
the Earth.
Chapter 7 - Review problems
Pages 269-273
#1, 2, 4, 14, 15, 16,26, 27, 29, 30, 31, 32, 33
Read Chapter 8
Chapter 8 Notes
Holt Physics
Pages 278-303
• Torque – a quantity that measures the
ability of a force to rotate an object
around some axis
• Lever arm – perpendicular distance from
the axis of rotation to a line drawn along
the direction of force
Torque = force x lever arm x angle of rotation
= F•d•(sinθ)
= torque
F = force
d = distance from applied
force to axis of rotation
θ = angle of rotation
Example – Trying to open a door by pushing or
pulling at the handle vs. trying to open the door
by pushing or pulling beside the hinge. Which is
harder?
** Torque is rotational work
** More torque is produced with a longer lever arm.
** When doing work, you want to maximize torque
by making the lever arm as long as possible,
thus making the rotation easier. Long wrench
vs. short wrench.
- Torque will be positive or negative based
on the direction of rotation
- Most simple machines rely on rotational
motion to work
Other Important Vocab Words
for Rotational Motion
Center of Mass – point at which all the
mass of the body can be considered to be
concentrated
Other Important Vocab Words
for Rotational Motion
Moment of Inertia – the measure of the
resistance of an object to change in
rotational motion
Yea, Homework!
Chapter 8 – Review problems
Page 282 – Practice 8A #1, 2
Pages 305-309
#1, 2, 3, 7, 8, 12