Download 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