Download Describing Rotational Motion

Describing Rotational Motion
Chapter 8
Linear to Rotational (Angular)
• Angular displacement: distance traveled around a
circle or arc (measured in radians or rad)
• Angular velocity: change in angular displacement
over time (measured in rad/s)
• Angular acceleration: change in angular velocity
over time (measured in rad/s2)
Linear to Angular (Rotational)
• We can use the same basic principles as before.
• The only difference will be the motion will be in a
circle rather than a straight line.
Torque
• A force that causes
an object to rotate
• Measures how
effective a force is in
rotating an object
• Measured in Newton
meters, Nm (in
America, known at
foot pounds, ft lb)
Time for Rotation
• Materials
Answer the following:
– Calculator
• How far does the second
• Objective
hand move every 10 s?
– Determine the angular
displacement and velocity • What is the angular velocity
of the hands on a clock.
for each hand (second,
minute, hour) in rad/s?
• Find angular displacement in
rad for each hand in 20 min?
• There is a speck of dust on
the second hand. Where on
the hand would it move the
fastest? The slowest?
Torque (Equation #1)
• Also known as force at a
distance from the equation:
t = F r sin q
t is torque (Nm)
F is force (N)
r is lever arm length or
radius (m)
q is the angle between F and
r (degrees)
Torque (Equation #2)
• Using the same argument as we did with
angular equations of motion, we can find
an angular equation for force.
• F  t (torque, Nm)
• m  I (moment of inertia, kgm2)
• a  a (angular acceleration, rad/s2)
F=mat=Ia
Moment of Inertia
• Known as rotational
mass
• Based on shape and
pivot point
• In general, a spinning
point-sized object will
have a moment of
inertia of m r2
• Units: kg m2
Torque Lab
Objective: Use
knowledge of torque to
balance.
Materials:
Meter stick
Binder clips
Masses
Hangers
Ring stand (clamp)
Procedures:
– Set-up equipment like demo
– Determine the mass of the
hanger holder using materials
given (___ g)
– Place hanger with 20 g at 70
cm
– Calculate and record where 50
g (silver hanger) should be
place on the other side for
balance (_____ cm)
– Place silver hanger at
calculated position
– Determine how close your
results were (off by ___ cm)
Ch8 Homework
72. 0.6 rad
75. 197 rad/s, 492 rad
82. 3.8 Nm
87. 63 N right, 37 N left
91. 21 rad/s, 16 rev,100 rad