AP PHYSICS
Rotational Motion
AIM
READ PAGES 194 – 217 (CHAPTER 8 ROTATIONAL MOTION)
READ PAGES 226 – 236 (CHAPTER 9 STATIC EQUILIBRIUM)
¢ What is rotational motion?
¢ What is angular displacement?
¢ What are angular velocity and acceleration?
¢ What is rotational kinematics?
¢ What is torque?
Torque problems
¢ What is static equilibrium?
¢ What is the moment of inertia?
¢ What is Conservation of Angular Momentum?
¢ What is rotational kinetic energy?
PRACTICE PROBLEMS
¢ What is the linear speed of a child on a merry-go-round
of radius 3.0 m that has an angular velocity of 4.0 rad/s?
PRACTICE PROBLEMS
¢ What is the angular velocity of an object traveling in a
circle of radius 0.75 m with a linear speed of 3.5 m/s?
FLIPPING PHYSICS VIDEO
PRACTICE PROBLEMS
¢ What is the angular acceleration of a ball
that starts at rest and increases its
angular velocity uniformly to 5 rad/s in 10
s?
PRACTICE PROBLEMS
¢ What is the angular velocity of a ball that
starts at rest and rolls for 5 s with a
constant angular acceleration of 20
rad/s2?
DAY 2
PRACTICE PROBLEMS
¢Achild pushes, with a constant force, a
merry-go-round with a radius of 2.5 m
from rest to an angular velocity of 3.0
rad/s in 8.0 s. What is the merry-go-
round's tangential acceleration?
PRACTICE PROBLEMS
¢ For the previous problem, what is the
merry-go-round's centripetal acceleration
at t = 8.0 s?
PRACTICE PROBLEMS
¢ What is the merry-go-round's total linear
acceleration for the previous problem at t
= 8.0 s?
PRACTICE PROBLEMS
¢A bear pushes, with a constant force, a
circular rock with radius of 7.2 m from
rest for 5.0 s. If the centripetal
acceleration of the rock at t = 5.0 s, is 4.0
m/s2, what is its angular velocity?
PRACTICE PROBLEMS
¢A tire with a radius of 4.0 m rolls with an
angular velocity of 8.0 rad/s. What is the
frequency of the tire's revolutions? What
is its period?
PRACTICE PROBLEMS
¢ Four different objects rotates with the
following parameters. In which cases are
the frequency of the objects' revolutions
identical?
Angular Speed and Velocity
Linear analogy: Linear analogy:
v=∆x a=∆v
∆t ∆t
PRACTICE PROBLEMS
¢A bicycle wheel with a radius of 0.30 m
starts from rest and accelerates at a rate
of 4.5 rad/s^2 for 11 s. What is its final
angular velocity?
PRACTICE PROBLEMS
¢A bicycle wheel with a radius of 0.30 m
starts from rest and accelerates at a rate
of 4.5 rad/s2 for 11 s. What is its final
linear velocity?
PRACTICE PROBLEMS
¢A bicycle wheel with a radius of 0.300 m
starts from rest and accelerates at a rate
of 4.50 rad/s2 for 11.0 s. What is its
angular displacement during that time?
PRACTICE PROBLEMS
¢A bicycle wheel with a radius of 0.30 m
starts from rest and accelerates at a rate
of 4.5 rad/s2 for 11 s. How many
revolutions did it make during that time
(note: 1 rev = 2π)?
PRACTICE PROBLEMS
¢A50.0 cm diameter wheel accelerates
from 5.0 revolutions per second to 7.0
revolutions per second in 8.0 s. What is its
angular acceleration?
PRACTICE PROBLEMS
¢A50.0 cm diameter wheel accelerates
from 5.0 revolutions per second to 7.0
revolutions per second in 8.0 s. What is its
angular displacement during that time?
PRACTICE PROBLEMS
¢A 50.0 cm diameter wheel accelerates uniformly
from 5 revolutions per second to 7 revolutions
per second in 8.0 seconds. What linear
displacement, s, will a point on the outside edge
of the wheel have traveled during that time?
EXAMPLE
A turntable capable of
angularly accelerating a = 12 rad / s 2
at 12 rad/s2 needs to be Dq = 400 rad
given an initial t = 6s
angular velocity if it is
to rotate through a net wo = ?
400 radians in 6 Dq = wot + 1 at 2
seconds. What must its 2
initial angular velocity 400 = wo (6) + (0.5)(12)(6) 2
be? wo = 30.7 rad/s
ANALOGIES BETWEEN LINEAR AND ROTATIONAL
MOTION
¢ There are many parallels between the motion equations for
rotational motion and those for linear motion
¢ Every term in a given linear equation has a corresponding
term in the analogous rotational equations
