Transcript Torque and Rotational Kinematics

Torque and Rotational Motion
HTHS AP Physics 1
M. Dimler
Torque
• Torque is a force that causes an object to turn
• Torque - Force directed perpendicular to the
“lever arm” of an object that has the ability to
rotate the object around a fulcrum or axis. Note:
this is usually an easy distance to visualize
τ = Fd
• Units of Torque are the Newton-Meter
Direction of the Torque Vector
• The Torque vector is perpendicular to both the
position vector and the force vector
• Right Hand Rule: point fingers of your right hand
in the direction of r vector (lever arm from center
of rotation), and bend your fingers in the
direction of the force vector. Your thumb then
points in the direction the torque vector.
• Positive torques cause ccw rotation, negative
torques cause cw rotation.
Net Torque
• When a force is not exactly acting
perpendicular to the “lever arm”, it needs to
be broken down into x and y components.
Net Torque
Equilibrium
• Static Equilibrium implies that the net force and
the net torque are zero, and the system is at rest.
• Dynamic Equilibrium implies that the net force
and the net torque are zero, and the system is
moving at constant translational and rotational
velocity
• Rotational Equilibrium implies that the net
torque on an object is zero.
Radians and Degrees
Once around a circle = 360° = 2π radians = 1 revolution = 1 rotation
Rotational Kinematics
• Angular Position
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Symbol (θ)
Units (radians)
Formula (θ=s/r)
s=θr
• Angular Displacement
– Symbol (Δθ)
– Units (radians/s)
– Formula (Δθ=θ2-θ1)
Practice Problem
1. A disk can rotate about its central axis like a merrygo-round. Which of the following pairs of values for
its initial and final angular positions, respectively,
give a negative angular displacement:
a) -3 rad,+5 rad
b) -3 rad, -7 rad
c) 7 rad, -3 rad
Rotational Kinematics
• Angular Velocity
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Symbol (ω)
Units (radians/sec)
Formula (ω=Δθ/Δt)
v=ωr
Note: Same at any point along disk
• Angular Acceleration
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Symbol (α)
Units (radians/sec2)
Formula (α=Δω/Δt)
at=αr and ar=v2/r=ω2r
Practice Problem
• Find the magnitude of the earth’s angular
velocity in radians per second. Then
determine the linear speed of an object on
the surface of the earth.
Practice Problem
• A bear rides a unicycle. If the unicycle wheel
begins at rest, and accelerates uniformly in a
ccw direction to an angular velocity of 15
rpms in a time of 6 seconds, find the angular
acceleration of the unicycle wheel.
Practice Problem
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What is the average angular velocity in the first two seconds?
What is the angular acceleration at 4 seconds?
What is the angular displacement during the 10 second interval?
AP Physics 1 MC Practice Problem
Center of Mass
Moment of Inertia
Derivation of I for a point mass
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½mv2 = ½Iω2
v=ωr
½ m(ωr)2 = ½Iω2
½ mω2r2 = ½Iω2
mr2 = I
Note: Units of I are kg∙m2
Moment of Inertia
(Rotational equivalent to mass)
Moments of Inertia can be added together to find the Moment
of Inertia of a system consisting of two or more objects.
∑I = I1 + I2
AP Physics I MC Practice
AP Physics I MC Practice
Newton’s 2nd Law for Rotation
Sample Problem
A 20-kg ladder of length 8m sits against a frictionless
wall at an angle of 60°. The ladder just barely keeps
from slipping.
a) Draw a FBD of the ladder.
b) Determine the force of friction of the floor on the
ladder.
c) Determine the coefficient of friction between the
ladder and the floor.
AP MC Practice Problem
AP Physics I MC Practice
Toilet Paper Roll Drop
Parallel Axis Theorem
Rotational Kinetic Energy
Conservation of Energy
Angular Momentum
• Angular Momentum is a measure of how difficult it is
to stop an object when rotating.
• Units of Angular Momentum: kg∙m2/s
Angular Momentum
The angular momentum of a point mass can be found by multiplying
the linear momentum of the point mass (p=m x v) by the
perpendicular distance from axis of rotation to the point mass (r).
L=rxmxv
Conservation of Angular Momentum
Angular Impulse
Bozeman Science Videos
http://www.bozemanscience.com/ap-physics
Click on the link above and watch the following
videos.
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Torque
Rotational Motion
Angular Momentum
Vector Properties of Angular Quantities
Angular Impulse
Conservation of Angular Momentum
Rotational Inertia
Aplusphysics.com Video Lessons
http://www.aplusphysics.com/courses/ap1/AP1_Physics.html#ap1
Click on the link above and watch the following
videos.
– Rotational Kinematics
– Torque
– Rotational Dynamics
– Angular Momentum
– Rotational Kinetic Energy
Twu Videos
• https://www.youtube.com/playlist?list=PLUn4
SDRnHn7cpTOIptsleLOSwhj4as8vm
There are 52 videos on the Rotational Motion playlist.
They are relatively short videos, so you should watch all
52 videos prior to next Unit test. You will be quizzed
twice a week to ensure you are pacing yourself.