Download Motion in Two Dimensions

Up to this point, balanced Forces meant no
acceleration….
100 N
Balanced
Forces?
Yes!
100 N
No Acceleration?
It will accelerate in a
spin!
Rotational Dynamics and Torque
A net force will cause and object to accelerate in
one dimension, but what about rotational
acceleration?
Would a Force exerted
at .5r from the center
produce the same
rotational acceleration
around the center
as…….
….. the same force exerted at
r from the center?
Forces that are not concurrent (same point) are
called Parallel Forces.
Parallel Forces exert Torque on an object.
Torque is the product of the Parallel Force and the
torque arm (lever arm) the force acts through.
τ=rxF
Units: Nm
What torque is exerted by a 55 kg bike rider who
puts all of his weight straight down on each pedal
if the pedal is 17 cm from the center of the
sprocket?
What force needs to be exerted on the end of a
torque wrench that is 35.0 cm long in order to
tighten a bolt to 80.0 Nm?
Explain why doorknobs are generally placed toward
the side of a door instead of in the middle of the
door.
A force of 5.00 N is used to turn a doorknob that
has a diameter of 6.70 cm. What torque does this
exert?
A torque of 3.25 Nm is required to pull open a
certain door. What force must be used to open this
door if the knob is located 75.0 cm away from the
hinge?
The mass exerts a torque of 23.0
Nm on the wheel which has a
diameter of 45.0 cm. How much
is the attached mass that produces
this torque?
The wheel on a car is held in place by four nuts.
Each nut should be tightened to 94.0 N∙m of torque
to be secure. If you have a wrench with a handle
that is 0.250 m long, what minimum force do you
need to exert perpendicular to the end of the
wrench to tighten a nut correctly?
Bob and Ray push on a door from opposite sides.
They both push perpendicular to the door. Bob
pushes 0.63 m from the door hinge with a force of
89 N. Ray pushes 0.57 m from the door hinge with
a force of 98 N, in a manner that tends to turn the
door in a clockwise direction. What is the net
torque on the door?
Rotational Inertia
An object will not start to spin unless a net torque
acts upon it.
A net torque would produce an
angular acceleration.
An object spinning at a constant rate will
accelerate if the mass is redistributed farther or
closer to the axis of rotation.
Rotational Inertia is the resistance of a rotating
object to changes in its rotational velocity-- it
depends on mass, distribution of mass, and the
axis of rotation!
The angular acceleration of an object will depend
directly upon the net torque, but inversely upon
the rotational inertia of the object:
= τ
I
therefore
τ=I
This is the rotational equivalent of Newton’s
Second Law (F = ma) for angular motion!
Rotational Inertia takes into account both the
shape, the mass and the rotation of a rotating
object!
Rotational Inertia, also called moment of inertia,
(kgm2) depends upon the mass and the axis of
rotation:
The farther the mass is concentrated from the
axis of rotation, the more rotational inertia
Ring and disk of
same mass and same
radius--Will they reach
the bottom at the
same time?
A wheel with a rotational inertia of .270 kgm2 is
accelerated from rest to 35.0 rad/s in 10.0 s. What
torque is required to accomplish this?
A force of 25.0 N is applied to a disk with a radius
of .300 m that is initially rotating at 38.0 rad/s. The
disk is stopped after having rotated 95.0 radians.
What is the rotational inertia of this disk?
A torque of 32.0 Nm is used to accelerate a sphere
of rotational inertia 175 kgm2. If the sphere is
accelerated to 8.66 rad/s in 20.0 s, what must have
been the original angular velocity of the sphere?
The pulley shown in the illustration
has a radius of 2.70 m and a moment
of inertia of 39.0 kg∙m2. The hanging
mass is 4.20 kg and it exerts a force
tangent to the edge of the pulley. What
is the angular acceleration of the
pulley?
A string is wound tight around the spindle of a top,
and then pulled to spin the top. While it is pulled,
the string exerts a constant torque of 0.150 N∙m on
the top. In the first 0.220 s of its motion, the top
reaches an angular velocity of 12.0 rad/s. What is
the moment of inertia of the top?