Rotation

1
Rotation Torque
BHS Science Opening the windows of possibilities!
2
Rotational Dynamics
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Rotational motion and angular motion are similar
  terms for the same type of motion -
• an object spinning around an axis.
• Differs from circular motion (discussed later)

3
Rotational Dynamics
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculations are similar to those of linear
  motion
• They are measured in different units but are
  analogous to one another in equation structure

4
Measuring rotational motion (displacement)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Angular displacement (Dq) can be measured in
  degrees, radians, or revolutions
• Usually radians
• (Dq Ds / r)
• (s arc length r radius)
• Conversion q (rad) (p/180o)q(deg)

5
Measuring rotational motion (angular speed)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Rate of displacement is called angular speed (w)
• The equation for average angular speed is
• w Dq /Dt

6
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• In terms of volume, the largest tree is the
  General Sherman at Sequoia National Park in
  California. Assuming the tree is perfectly
  circular, its radius at the base is 5.55 m. If
  you were allowed to walk 31.3 m counterclockwise
  along the side of the tree, what would your
  angular displacement be?

7
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• The propellers, or screws, of a steamship push
  water away from the ship, causing the ship to
  move forward. Suppose a ships screw turns 106
  rad clockwise in 7.5 s. What is the average
  angular speed of the screw?

8
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• The earth has an equatorial radius of
  approximately 6380 km and rotates 360o every 24
  hours.
• What is the angular displacement of a person
  standing at the equator for 1.0 h?
• Convert this to radians.
• What is the arc length traveled by this person?
• What is his angular speed?

9
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Do now problems 1 on both pp. 247 248

10
Measuring rotational motion (angular acceleration)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Like linear motion, angular motion can also have
  acceleration (a). The equation is

11
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• A turntable has an average angular acceleration
  of 1.5 rad/s 2 and an initial angular speed of
  3.0 rad/s. What is the turntables angular speed
  4.0 s later?

12
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• The gasoline engine for a power lawnmower has an
  average angular acceleration of 32 rad/s2 when
  first started. What is the engines angular speed
  after 1.5 s, assuming an initial angular speed of
  0 rad/s?

13
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• A toy consists of a windup car and a circular
  metal base with a shallow groove that guides the
  car in a circular path. At first the car has an
  angular speed of 7.14 rad/s, but after 9.00 s its
  angular speed is 2.38 rad/s. What is the cars
  average angular acceleration?

14
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Because of the gravitational forces between Earth
  and the moon, the angular speed of Earth is
  decreasing at about 1.7 x 103 s each century.
  This means that 70.0 million years ago, Earth
  made one complete rotation in just 23.66 h,
  whereas now it takes 24.00 h. What is Earths
  average angular acceleration over the last 70.0 x
  106 years?

15
Measuring rotational motion (kinematics)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Kinematics equations for rotational and linear
  are similar

16
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• A model airplane is kept in a circular path by
  means of a control line. The airplane starts at
  rest and reaches an angular speed of 3.33 rad/s
  after a constant angular acceleration of 0.183
  rad/s2. How long does it take the airplane to
  reach its final angular speed?

17
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Even rarer than phonograph turntables for
  long-playing (LP) records are those turntables
  used in the first half of the twentieth century.
  Unlike the LP turntables, which rotated at 33.3
  rev/min, these older turntables turned at 78.0
  rev/min. Suppose a turntable with this angular
  speed is shut off, so that it comes to a stop
  30.0 s later. If the turntable has a constant
  angular acceleration of 0.272 rad/s2, what is
  its angular displacement?
• (Give your answer in both radians and number
  of revolutions.)

18
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• An automobile engines angular speed is increased
  from 1200 rev/min to 3600 rev/min in 12 s. What
  is the engines angular acceleration in rad/s2?

19
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Do now Problem 1 on both pp 250 and 252.

20
Measuring rotational motion (practice)
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Due tomorrow
• ALL Problems on pp 247, 248, 250 and 252.

21
Tangential and centripetal motion
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Tangential refers to the linear speed of an
  object or point on a rotating object as it turns.
• The term tangent refers to the speed tangent to
  the object's path.

22
Tangential and centripetal motion
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!
23
Tangential Speed
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• v r w

24
Tangential Speed
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• v r w
• v r (Dq / t)

25
Tangential Speed
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• v r w
• v r (Dq / t)
• v r (Ds/r) / t

26
Tangential Speed
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• v r w
• v r (Dq / t)
• v r (Ds/r) / t
• v (Ds) / t

27
Tangential Speed
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• v r w
• v r (Dq / t)
• v r (Ds/r) / t
• v (Ds) / t
• Or v Dd / Dt

28
Tangential Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• a r a

29
Tangential Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• a r a
• a r (Dw/ Dt)

30
Tangential Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• a r a
• a r (Dw/ Dt)
• a r (Dq / Dt)/ Dt

31
Tangential Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• a r a
• a r (Dw/ Dt)
• a r (Dq / Dt)/ Dt
• a r (Ds/r / Dt)/ Dt

32
Tangential Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• a r a
• a r (Dw/ Dt)
• a r (Dq / Dt)/ Dt
• a r (Ds/r / Dt)/ Dt
• a (Ds/ Dt2)

33
Tangential Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Calculated by
• a r a
• a r (Dw/ Dt)
• a r (Dq / Dt)/ Dt
• a r (Ds/r / Dt)/ Dt
• a (Ds/ Dt2)
• Or a Dd / Dt2

34
Practice
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Do 255 and 256.

35
Centripetal Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• center seeking acceleration of an object
  moving in a circular path at a constant speed.
• ac vt2 / r and
• ac r w2
• Practice p 258.

36
Force that causes Centripetal Acceleration
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Centripetal force
• Fc m ac m(vt2 / r ) or
• Fc m (r w2)
• Practice p 261

37
Lab
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Do centripetal force lab.
• Due tomorrow

38
The big centripetal force - Gravity
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Gravity is one of the four fundamental field
  forces
• All masses have a gravitational field

39
The big centripetal force - Gravity
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• The equation is
• Fg G (m2 m2) / r2
• Force increases with mass
• Forces decreases with distance It is an
  inverse square law that is, it diminishes
  proportional to the square of the distance

40
The big centripetal force - Gravity
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Fg G (m2 m2) / r2
• Practice p. 265
• You should be through 15 on the study guide

41
Torque
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Torque is a force that causes rotational motion
• Ex. A wrench turning a bolt or a lever lifting a
  heavy rock.

42
Torque
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Torque is a function of both the force applied
  and the length of the lever arm
• Torque ( T ) F x L

43
Torque
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Net Torque like net force this is the
  difference between the opposing torques acting on
  an object

44
Center of Mass
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• This is the point at which all of an objects
  mass can be considered to be concentrated.
• If you support this point, you support the
  object.

45
Center of Mass
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Key Phrase if an object is described as
  uniform that means that its mass distributed
  evenly and therefore its center of mass is in the
  physical center.

46
Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Equilibrium occurs when all forces both
  translational and rotational are balanced.
• Net F 0 and Net T 0
• The first law of motion still applies
• So, what do we know of the motion?

47
Static Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• This equilibrium occurs in solid structures such
  as bridges, buildings, etc. that are meant to be
  static (i.e. not moving)
• In this situation there is both rotational
  equilibrium and translational equilibrium

48
Static Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Rotational equilibrium
• Tcw Tccw
• Translational equilibrium
• Fup Fdown and
• Fleft Fright and
• Fforward Fback

49
Torque
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Force down Force down
• Left Right

50
Torque Translational Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Force down Force down
• Left Right
• Upward force

51
Torque
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Counter
• Clockwise Clockwise
• Torque Torque

52
Torque Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Force down Force down
• Left Right
• Upward
  force

53
Torque Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Sign hanging from a pole

wall
tension
compression
weight
54
Torque Equilibrium
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Door

c.m.
H Wall H
tension
weight
compression
55
And the test is . . .
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Angular motion
• Tangential motion
• Centripetal force and acceleration
• Newtons Law of Universal Gravitation
• Torque
• Statics

56
Tangential and centripetal motion
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!
57
Tangential and centripetal motion
Momentum Opening the windows of
possibilities!
Rotation Torque BHS Science - Opening
the windows of possibilities!

• Link to Video
• http//www.teachertube.com/view_video.php?viewkey
  861d4199ca0372b9f96c