Transcript Chapter 8 - StrikerPhysics

Chapter 8
Rotational Motion and Equilibrium
Rigid Body
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An object or system of particles in
which the distances between particles
are fixed.
Translational (sliding) and rotational
(spinning) motion becomes relevant
when we consider rigid bodies.
Translational vs Rotational
Motion
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Translational Motion: Every particle in
the rigid body has the same
instantaneous velocity (no rotation).
Rotational Motion: Every particle in
the rigid body has the same angular
velocity and travels in circles around a
fixed axis.
Rotation and Translation
Rolling Motion
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Rolling without slipping is a
combination of rotation and
translation.
Torque
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A force is necessary to produce changes in rotational
motion as well as translational.
In pure translational motion, the translational
acceleration is proportional to the net force. Fnet = ma
In pure rotational motion, the angular acceleration is
related to the net force AND to the perpendicular
distance between the axis of rotation and the line of
action. We call this distance the lever arm or r
Torque Terminology
Line of Action – an imaginary line
extending through the force vector
Lever Arm – r - the perpendicular
distance from the axis of rotation to
the line of action
Line of Action and Lever Arm
Line of Action and Lever Arm
Torque
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Torque = (lever arm distance)·(Force)
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Torque = r ·F
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Torque = r F sinθ
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T = r F sin θ
Torque Direction
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The right hand rule can be used to find the
direction of Torque as r X F
T=rxF
Alternatively, torques that cause
counterclockwise rotation are taken to be
positive and torques causing clockwise
rotation are taken to be negative.
Torque
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T = r F sin θ
Torque is a vector, r is a vector and F
is a vector!
Torque is measured in [m·N]
The unit for Torque is NOT equivalent
to a Joule [N·m]
Right hand rule can be used to find
the direction of torque.
Examples
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When you lift up on something with
your forearm, torque is applied on the
lower arm by the biceps muscle. With
the axis of rotation through the elbow
joint and the muscle attached 4.0 cm
from the joint, what is the torque if
the muscle exerts 600N of force?
Equilibrium
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Balanced forces create translational
equilibrium.
Balanced torques create rotational
equilibrium.
Mechanical equilibrium occurs when forces
and torques balance.
Static equilibrium occurs when a rigid body
is at rest and forces and torques balance.
Example
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A picture hangs motionless on a wall.
The picture has a mass of 3.0 kg.
Find the magnitude of the tension in
the wires if one wire makes a 50°
angle and the other wire makes a 45°
angle.
Example: Rotational
Equilibrium
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Three masses are suspended from a
meter stick balanced at the halfway
point . 25g hangs from 0 cm and 75g
hangs from 20cm. Unknown mass
hangs at 85cm. Neglecting the mass of
the meter stick, how much mass must
be suspended on the right side for the
system to be in static equilibrium?
Example
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A ladder with a mass of 15 kg rests
against a smooth wall. A painter who
has mass 78 kg stands on the ladder
as shown. What is the magnitude of
the frictional force that acts on the
bottom to keep the ladder from
sliding?