Transcript Rotation - TeacherWeb

Rotation
Another Kind of Motion
Rotational Motion
 Applies to rigid bodies
 Also to liquids and gases
 All points move in circles about a line called axis
of rotation
Angular Quantities
q = l/r
 In radians
 2pr = 360 deg
 1 radian = 57.3 deg
 Angular velocity(average) =
w = Dq/Dt
(omega)
 Angle
l
q
r
More Angular Quantites
 Angular acceleration(average)
a = Dw/Dt
 Linear velocity v = rw
 Frequency of rotation f = w/2p
 Units: Hertz = rev/sec
 Period T = 1/f
Torque
 Produces rotation
 The rotational analog of force
 Depends on direction and where applied
 Equals force times lever arm times sine of angle
between them t = rFsinq
 Unit is meter Newton
 Lever arm is perpendicular distance of axis of
rotation to line of action of force
Torque
t = rFsinq
Lever arm
r
Axis of
rotation
q
F
How to get the most torque
 What angle gives the most torque?
 Where should you hold the wrench?
Balanced Torques
 Net torque produces acceleration
 When torques are balanced we have rotational
equilibrium
 Torques act to rotate a system clockwise or
counterclockwise
Example
 A meter stick rests on a pivot at the center.
A 1.0
Newton weight is attached at the 20cm mark.
Where must a 2.0 Newton weight be hung on the
other side of the string to balance it? (hint: draw
it)
 Ans.
at 65 cm, 15 cm from pivot or fulcrum
Angular Momentum
 Analog of linear momentum mv
(like mv in linear motion)
 I is rotational inertia or moment of inertia
 I = mr2 for a particle
 L = mr2w for single particle (=mvr)
 Angular momentum is conserved
 L = Iw
How does skater speed rotation?
 L = Iw
= constant