chapter 8.1 and 8.2 torque and angular rotation. definition of torque torque is the quantity that...
TRANSCRIPT
Chapter 8.1 and 8.2Torque and Angular Rotation
Definition of TorqueTorque is the quantity that measures the
ability of a force to rotate an object around some axis (fulcrum). ◦ Units – Nm
Lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force.
Torque depends on Force and the length of the lever arm.
Torque = Force x lever arm τ = Fr
Torque (cont.)◦Only the perpendicular component of
the force produces a torque.◦The lever arm is the distance
between the point where the force is applied and the axis of rotation (known as the fulcrum).
◦By convention, we treat counterclockwise torque as positive, clockwise as negative.
◦Torque like displacement and force is a vector quantity
Sample problem 1Find the torque produced by a 3 N
force applied to a door at a perpendicular distance of 0.25 m from the hinge.◦Known?
F = 3N, d = 0.25m
◦Unknown? τ = ?
◦Equation? τ = Fd τ = 3 (.25) = 0.75 Nm
Torque problem 2 In the picture below, the person on the left weighs
900 N, and the person on the right weighs 400 N. If the person on the right is sitting 3 m from the fulcrum and the seesaw is balanced, how far must the person on the left be from the fulcrum? ◦ Known: Equation: Fr = Fr
◦ Unknown:
Chapter 8.3Center of Mass
The Center of Mass
SECTION
8.3 Equilibrium
The center of mass of a person varies with posture.
For a person standing with his or her arms hanging straight down, the center of mass is a few centimeters below the navel, midway between the front and back of the person’s body.
The Center of Mass of a Human Body
SECTION
8.3 Equilibrium
When the arms are raised, as in ballet, the center of mass rises by 6 to10 cm.
SECTION
8.3 Equilibrium
The Center of Mass of a Human Body
By raising her arms and legs while in the air, as shown below, a ballet dancer moves her center of mass closer to her head.
SECTION
8.3 Equilibrium
The Center of Mass of a Human Body
The path of the center of mass is a parabola, so the dancer’s head stays at almost the same height for a surprisingly long time.
SECTION
8.3 Equilibrium
The Center of Mass of a Human Body
Center of Mass and Stability
Click image to view movie.
SECTION
8.3 Equilibrium