Transcript Circular Motion PowerPoint

Circular Motion
Centripetal Force
Key Question:
Why does a roller coaster stay on a track upside down on a loop?
Centripetal Force
• We usually think of acceleration as a change in speed.
• Because velocity includes both speed and direction, acceleration can also be a change in the
direction of motion.
Centripetal Force
• Any force that causes an object to move in a circle is called a centripetal force.
• A centripetal force is always perpendicular to an object’s motion, toward the center of the circle.
Centripetal Force
Mass (kg)
Centripetal
force (N)
Fc = mv2
r
Linear speed
(m/sec)
Radius of path
(m)
Calculate centripetal force
• A 50-kilogram passenger on an amusement park ride stands
with his back against the wall of a cylindrical room with radius
of 3 m.
• What is the centripetal force of the wall pressing into his back
when the room spins and he is moving at 6 m/sec?
Centripetal Acceleration
• Acceleration is the rate at which an object’s velocity changes as the
result of a force.
• Centripetal acceleration is the acceleration of an object moving in a circle
due to the centripetal force.
Centripetal Acceleration
Centripetal
acceleration (m/sec2)
ac = v2
r
Speed
(m/sec)
Radius of path
(m)
Calculate centripetal acceleration
• A motorcycle drives around a bend with a 50-meter radius
at 10 m/sec.
• Find the motor cycle’s centripetal acceleration and
compare it with g, the acceleration of gravity.
Centrifugal Force
 We call an object’s tendency to
resist a change in its motion its
inertia.
 An object moving in a circle is
constantly changing its direction
of motion.
• Although the centripetal force pushes you toward the center of
the circular path...
• ...it seems as if there also is a force pushing you to the outside.
This apparent outward force is called centrifugal force.
Centrifugal Force
 Centrifugal force is not a true
force exerted on your body.
 It is simply your tendency to
move in a straight line due to
inertia.
• This is easy to observe by twirling a small object at the end of a
string.
• When the string is released, the object flies off in a straight line
tangent to the circle.
Torque
• The door is free to rotate about an axis through O
• There are three factors that determine the effectiveness
of the force in opening the door:
• The magnitude of the force
• The position of the application of the force
• The angle at which the force is applied
Torque, cont
• Torque, t, is the tendency of a force to rotate an object about
some axis
• t=rF
• t is the torque
• F is the force
• symbol is the Greek tau
• r is the length of the position vector
• SI unit is N.m
Direction of Torque
• Torque is a vector quantity
• The direction is perpendicular to the plane determined by the
position vector and the force
• If the turning tendency of the force is counterclockwise, the torque
will be positive
• If the turning tendency is clockwise, the torque will be negative
Multiple Torques
• When two or more torques are acting on an object, the
torques are added
• As vectors
• If the net torque is zero, the object’s rate of rotation doesn’t
change
General Definition of Torque
• The applied force is not always perpendicular to the position
vector
• The component of the force perpendicular to the object will
cause it to rotate
General Definition of Torque, cont
• When the force is parallel to the position vector, no
rotation occurs
• When the force is at some angle, the perpendicular
component causes the rotation
General Definition of Torque,
final
• Taking the angle into account leads to a more general
definition of torque:
• t = r F sin q
• F is the force
• r is the position vector
• q is the angle between the force and the position vector
Lever Arm
• The lever arm, d, is the perpendicular distance from the
axis of rotation to a line drawn along the direction of the
force
• d = r sin q
Right Hand Rule
• Point the fingers in the
direction of the
position vector
• Curl the fingers
toward the force
vector
• The thumb points in
the direction of the
torque
Force vs. Torque
• Forces cause accelerations
• Torques cause angular accelerations
• Force and torque are related