Transcript Physics_AP_A_Evans_Day_39_Period_2

AP Physics B I.E
Circular Motion and Rotation
I.E.1 Uniform Circular Motion
Behold the ball moving in a circular
path: Who will it hit?
Ex. Find the speed of the earth at the equator as it rotates
about its axis if the radius of the earth is 6.37 EE 6 m.
Centripetal acceleration is a
vector, directed toward the center
of the circle.
Centripetal force always points
towards the center of the circle
and continually changes
directions as the object moves. It
is not a new force. It is merely
the way we describe the net force
pointing towards the center of the
circle.
What is the centripetal force for . . .
• The clothes in a washing machine that is in
the “spin” cycle?
• A car making a circular turn?
• A roller coaster making a circular turn?
• The “Gravitron”?
• The Earth as it orbits the Sun?
Ex. An object of mass 5.0 kg moves at a constant speed of 6.0
m/s in a circular path of radius 2.0 m. Find the object’s
acceleration and the force that keeps it moving in a circular
path.
Ex. A 10.0 kg mass is attached to a string that has a breaking
strength of 200 N. If the mass is whirled in a horizontal
circle of radius 80 cm, what maximum speed can it have?
Ex. Car on a Curve: A car travels with a velocity of 13.4 m/s
on a level circular track with a radius of 50.0 m. What is the
coefficient of static friction between the car and the road in
order to make the circular turn without sliding?
Ex. A roller coaster car has a speed of 15 m/s at the top of a
circular loop (where the car is upside down). If the diameter of
the loop is 40.0 m and the total mass of the car and passengers
is 1200 kg, find the magnitude of the normal force exerted by
the track on the car.
Ex. What is the normal force for the roller coaster when the
car is at the bottom of the circle?
Concept Question: A roller coaster makes a vertical loop.
What is the direction of the acceleration of the coaster at the
a) top of the loop? b) bottom of the loop?
Concept question: Is it harder for a
trapeze artist to hold his partner
when hanging vertically at rest, or
swinging through the bottom of the
arc?
Ex. A 0.150 kg ball on the end of a 1.10 m long string is swung
in a vertical circle. a) Find the minimum speed the ball must
have at the top of the circle to maintain its circular path. b)
Calculate the tension of the string at the bottom of the circular
path if the ball is moving at twice the speed in part a.
Concept Question: A ball attached to a string is whirled in a
horizontal circle with radius r. If the radius of the string is
changed to ½ r and the same centripetal force is applied to
the string, what is the new speed of the ball?
Ex. A car with mass m and speed v, and a second car with
mass 1/2m and speed v, both travel the same horizontal
circular path. If the frictional force required to keep the
larger car on the road is F, what is the frictional force
required to keep the smaller car on the road without
skidding?
I.E.2 Torque and Rotational
Statics
Which force will rotate the rod,
fixed at the left end?
F3
F4
F2
pivot
F1
Torque is that which creates
rotation. What are three factors
that affect torque?
Now, using the formula, explain
why only F4 produces torque.
Ex. A student pulls down with a force of 40 N on a rope that
winds around a pulley of radius 5.0 cm. What is the torque
produced?
If a body is in equilibrium, neither
its linear (translational) motion,
nor its rotational motion changes.
So, ΣF = 0 and Στ = 0.
By convention, ccw torques are
positive and cw torques are
negative.
Ex. What is the net torque on the cylinder below which
rotates about its center?
F1 = 100 N
F2 = 80 N
8 cm
12 cm
Ex. An object weighing 60 N is set on a rigid beam of
uniform mass, and a weight of 10 N, rests on a pivot, as
shown below. What is the magnitude of the vertical force
that must be applied at the right end of the beam to keep
it from rotating?
F
60 N
4m
6m