Download Zero Torque and Static Equilibrium

Zero Torque and Static Equilibrium
If the net torque is zero, it doesn’t matter which axis we consider rotation to be around; we are free to choose the one that makes our calculations easiest.
1
How do we incorporate the plank into the problem?
Recall when an object has a
symmetric shape and its mass is
uniformly distributed, the center
of mass is located at the
geometric center.
The center of mass for any
extended object provides the
distance from the axis of rotation
of the resultant torque from
gravitation forces acting on every
point on that object.
L/2
mp g
Total force acting on the plank =0
Total torque acting on the plank =0
Torque equation involves only 1 unknown force F2
Solve for F2
Substitute F2 into the force equation and solve for F1
2
What is the maximum distance x from a smooth frictionless wall you can put a 100N uniform ladder of length 5.0m on a floor where the coefficient of static friction is 0.40? The equilibrium condition
the force exerted by the wall is equal to the force of friction
the normal force Fn determines the maximum force of static friction
x
Choose ground‐ladder interface as pivot point, but you could choose any point and the result would remain the same. The sum of the torques must equal zero because we are in equilibrium.
Substitute for
3
Rotational Kinetic Energy and the Moment of Inertia
The total kinetic energy of a rolling object is the sum of its linear and rotational kinetic energies: The second equation makes it clear that the kinetic energy of a rolling object is a multiple of the kinetic energy of translation.
An object starts at rest at the top
of an incline plane and rolls
without slipping to the bottom
What is the object’s speed on reaching the bottom?
v
Equating initial and final energy we have the relationship
Solving for v
Conservation of Energy
If these two objects, of the same mass and radius, are released simultaneously, the disk will reach the bottom first – more of its gravitational potential energy becomes translational kinetic energy, and less rotational.
Vi =0
Water and Ice Bottle Race
vf
Independent
of R and M
vf
I = 0 for water bottle
I = ½ MR2 ice bottle
7
A block with mass m1 of 2.4kg is connected to 2nd block of m2=1.8 kg by a rope
wrapped around a pulley of mass m3=3kg and radius of R=15cm. If d=20cm, what is
the speed of m2 just before hitting the ground?
8
9
rolling
sphere
A, vA=0
D, vD
h
B, vB
R
2R
y
y
x
C, vc=max velocity
y=0, U=0
Point B:
let y be a variable for every point
Point D:
(1)
However there is an addition condition for point D for the ball to stay on the track
(2)
(1)
Substitute
equation (2)
for vD
Min criteria
Solve for h
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