Click here to load reader
Upload
katherine-heigl-madrigal
View
279
Download
15
Tags:
Embed Size (px)
DESCRIPTION
Circu
Citation preview
*Property of STI H0055
Circular Motion and Rotational Motion Angular Quantities
Uniform Circular Motion
Rotational Motion
Center of Gravity
Angular Momentum
Torque
H0055
1 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Angular QuantitiesAngular Position/Displacement
1. Angular Position (θ)
Denotes the orientation of object in space (rotation)
Direction of the displacement vector drawn from the axis to the location of the object (revolution)
2. Angular Displacement (Δθ)
Change in angular position
Difference between initial (θi) and
final (θf) angular positions
Δθ = θf -θi
2 _______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Angular QuantitiesAngular Velocity
Rate of change in object’s angular position
Angular displacement per unit of time t
t
Angular Acceleration
Rate at which the angular velocity changes:
where ωf and ωi are the final and initial angular velocities
respectively
t
if
3 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Find the angular
velocity of a sprinter
that makes two laps
around an oval in
10.0 minutes.
4 _______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
A compact disc makes 500
revolutions per minute. If
the CD accelerates
uniformly in 4.0 seconds
from rest, what is its
angular acceleration in
radians per second?
5 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Angular quantities as vectors
Angular velocity and angular acceleration are
vectors
↑ ω = same direction as α
↓ ω = opposite direction of α
Right-hand rule
6 _______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Angular quantities as vectors
7 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Angular quantities as vectors
Angular displacement is not a vector quantity
Addition of angular displacements is not
commutative
8 _______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Uniform Circular Motion
Movement of an object along a circular path
with constant speed and constant angular
velocity
9 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Tangential Speed (v)
Speed of an object along a circular path
where v is the tangential speed, r is the radius of
the circular path and t is the time
t
Δθrv
10 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Tangential Speed (v)
Other equations:
ωrv
fT
v r2r2
Tf
1
T = period of revolution
f = frequency
11 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Centripetal Acceleration (ac)
Acceleration of object moving in a circular path
Always directed towards the center
Not denoted as a vector because its direction is
never constant
r
v 2
= a c
r2= a c
2
24= a c
T
r
Formulas:
12 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Centripetal Force (Fc)
Force that causes the object to move in circular path
Always have the same direction as ac
It is not denoted as vector because its direction is never constant
r
vm =Fc
2
r =mFc
2
2
24
T
r =mFc
Fc = mac
Formulas:
13 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
14 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
A 40 kg child makes 10 revolutions around the
Cliffhanger in 29.3 seconds. The radius of the barrel
is 2.9 meters, what is the centripetal force acting on
the child?
15 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
A 0.035 kg pebble is made to whirl in a circular
path at the end of a 1.00 m string. What is the
tangential velocity if the pebble makes one
revolution in 1.50 s? What is the centripetal
acceleration? What is the tension in the string?
16 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Centrifugal Force
Not a real force, but experienced as if they are
actual force
Arises due to inertia
Objects tend to resist centripetal force and
move in straight path
17 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Rotational Motion Rotation
Movement of an object along its axis causing it
to change its orientation in space
Translational Motion
Movement of an object along a path causing it
to change its location in space
18 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Rotational Inertia
Tendency to resist any change in rotational motion
Depends on the distribution of mass in relation to the
axis
The farther is the bulk of mass from the axis, the
greater is the rotational inertia
Expressed using Newton’s Second Law for Rotational
Motion
t = I a
I = rotational inertia
t = the torque
a = the angular acceleration
19 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
20 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Center of Gravity
A point within the object which when used as a
pivot point will result in balanced torque and
hence will not cause any rotation
May lie at a point within the object where there
is no mass
21 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Angular Momentum
The product of the moment of inertia I
and the angular velocity
L = I
“An object or system of objects will maintain
its angular momentum unless acted upon
by an unbalanced external torque.”
22 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Law of Conservation of Angular Momentum
If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant
23 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Cross Multiplication
Type of vector multiplication where the product of two vectors a and b is another vector c, such that c lies perpendicular to the plane of a and b
c = a × b
Magnitude of c is determined by the formula:
where θ is the angle between a and b
Direction is determined by right-hand rule
Not commutative
sinabc
24 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
25 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Torque (τ) Force acting at a certain distance away from the axis;
this distance is called lever arm
The cross-product of force and lever arm:
τ = F × r τ = Fr sinθF = force
r = lever arm
θ = the angle between them
unit of torque is Newton meter (N m)
F
r
θ
26 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
27 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
You pull the door open with a
perpendicular force of 10.0 N.
Your hand is 0.400 m away
from the door hinge. How
much torque is produced?
28 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Solve for the torque due to a force of 15 N on a
body if the lever of arm is 0.75 m in length.
29 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
Rotational Equilibrium
An object is in rotational equilibrium if the sum
of all torques acting on it is zero
0321 NET
30 ______________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
*Property of STI H0055
At what distance from the center of the seesaw
should a man weighing 75.0 kg sit in order to
balance the seesaw while a 30.0 kg child is sitting
on the other side 2.0 m away from the center?
31 _____________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________