Physics 2111 Unit 16 - College of DuPage · Physics 2111 Unit 16 Today’s Concepts: a) Work and KE...
Transcript of Physics 2111 Unit 16 - College of DuPage · Physics 2111 Unit 16 Today’s Concepts: a) Work and KE...
Physics 2111
Unit 16
Today’s Concepts:
a) Work and KE in rotations
b) Angular Acceleration
Physics 211 Lecture 16, Slide 1
Where are we?
Mechanics Lecture 3, Slide 2
Rotational Motion and what
causes it.
Note that we’re going to
do statics last (after
angular momentum)
summary so far
Mechanics Lecture 14, Slide 3
x
dx/dt = v
dv/dt = a
q
dq/dt = w
dw/dt = a
m I
F t
S F = ma S t = Ia
න Ԧ𝐹 ∙ 𝑑 Ԧ𝑥
KEY POINT
Mechanics Lecture 14, Slide 4
KETotal = KEtrans + KErot
= ½ mv2com + ½ Icomw2
motion of the center of mass
motion Around the center of mass
An object can have one… or the other…. or both.
Mechanics Lecture 15, Slide 5
A long length of string is wrapped around
5kg drum with a radius of 30cm. The
drum is free to spin around a frictionless
axle. After the string has been pulled with
a 10N force for a distance of 5m, what is
the angular velocity of the drum?
Example 16.1 (drum)
M1=5kg
10N
Example 16.2 (pulley and mass - again)
Mechanics Lecture 15, Slide 6
A long length of string is wrapped around
5kg drum with a radius of 30cm. The
drum is free to spin around a frictionless
axle. The other end of the string is
attached to a 10kg mass. If angular
velocity of the pulley after the mass has
dropped 2m?M1=5kg
M2=10kg
Mechanics Lecture 15, Slide 7
A long length of string is wrapped around 5kg
disk with a radius of 50cm. The disk not pinned
and sits on a frictionless surface. The string is
pulled by a 10N force. What is the translation
velocity of the point on the top rim of the disk (A)
1.5 seconds after the force is applied?
Example 16.3 (unpinned disk)
M1=5kg
A
+
Mechanics Lecture 15, Slide 8
A long length of string is wrapped around 5kg
disk with a radius of 50cm. The disk not pinned
and sits on a frictionless surface. The string is
pulled by a 10N force. What is the translation
velocity of the point on the bottom rim of the
disk (B) 1.5 seconds after the force is applied?
Question
M1=5kgB
A) 9m/sec
B) 6m/sec
C) 3m/sec
D) 0m/sec
E) -3m/secvTAN vCOM
+
Mechanics Lecture 15, Slide 9
A long length of string is wrapped around 5kg disk
with a radius of 50cm. The disk not pinned and
sits on a frictionless surface. The string is pulled
by a 10N force. What is the translation velocity of
the point on the right rim of the disk (C) 1.5
seconds after the force is applied?
Example 16.3(b) (unpinned disk)
M1=5kg
C
vTAN
vCOM+
Mechanics Lecture 15, Slide 10
=
Rolling without slipping
w = vcom/r
+
Has both KErot and KEtran
Example 16.4 (disk on ramp)
A cylinder rolls down a 1m high and 2m long ramp. The coefficient of static friction between the cylinder and ramp is ms=0.5. What is the velocity of the center of mass of the cylinder at the bottom of the ramp?
Mechanics Lecture 16, Slide 11
2m
1m
Question
Mechanics Lecture 16, Slide 12
Which of the following best represents the FBD of the cylinder as it’s rolling down the ramp?
(A) (B) (C) (D) (E)
Question
Mechanics Lecture 16, Slide 13
Which of the following statements is true of the cylinder as it’s rolling down the ramp?
A) SF=maB) St=IaC) Both (A) and (B)D) Neither (A) or (B)
Example 16.4 (disk on ramp)
A cylinder rolls down a 1m high and 2m long ramp. The coefficient of static friction between the cylinder and ramp is ms=0.5. What is the velocity of the center of mass of the cylinder at the bottom of the ramp?
Mechanics Lecture 16, Slide 14
2m
1m
Q
Question
As the disk is rolling down the ramp, what the value of the force of static friction?
A) mg ms
B) mg sinQ ms
C) mg cosQ ms
D) mg tanQ ms
E) We can’t get the force of static friction just using these equations
Q
Example 16.4 (disk on ramp)
A cylinder rolls down a 1m high and 2m long ramp. The coefficient of static friction between the cylinder and ramp is ms=0.5. What is the velocity of the center of mass of the cylinder at the bottom of the ramp?
Mechanics Lecture 16, Slide 16
2m
1m
CheckPoint
Mechanics Lecture 16, Slide 17
A cylinder and a hoop have the same mass and radius. They are released at the same time and roll down a ramp without slipping. Which one reaches the bottom first?
A) Cylinder
B) Hoop
C) Both reach the bottom at the same time
Prelecture question
Mechanics Lecture 11, Slide 18
A block and a ball have the same mass and
start at rest at the top of identical ramps.
The block slides down the ramp without
friction and the ball rolls down the ramp
without slipping.
Which one has the most kinetic energy at
the bottom of the ramp?
A) the ball
B) the block
C) the same
Acceleration depends only on the shape, not on mass or radius.
What you saw in your PreLecture:
Mechanics Lecture 16, Slide 19
Question
Mechanics Lecture 16, Slide 20
A) Small cylinder
B) Large cylinder
C) Both reach the bottom at the same time
A small light cylinder and a large heavy cylinder are released at the same time and slide down the ramp without friction. Which one reaches the bottom first?
CheckPoint
Mechanics Lecture 16, Slide 21
A block and a ball have the same mass and move with the same initial velocity across a floor and then encounter ramps of identical size. The block slides without friction and the ball rolls without slipping. Which one makes it furthest up the ramp?
A) Block
B) Ball
C) Both reach the same height.
v
vw
Three blocks connected by strings are pulled across a frictionless surface by a force F.
Compare the magnitudes of the accelerationof the three masses:
Question
Mechanics Lecture 16, Slide 22
T1 T2
R
m1m2 m3
A) a1 > a2 >a3
B) a1 = a2 = a3
C) a1 < a2 <a3
D) a1 < a3 <a2
F
Three blocks connected by strings are pulled across a frictionless surface by a force F.
Compare the magnitudes of the force and the tension in the strings:
Question
Mechanics Lecture 16, Slide 23
T1 T2
R
m1m2 m3
A) F > T2 >T1
B) F = T2 = T1
C) F < T2 <T1
D) F1 < T1 <T2
F
Two blocks connected by strings which is looped over a pulley of mass m2 and radius r. m1 sits on a frictionless table and m3 is acted by the force of gravity Fgrav.
Compare the magnitudes of the accelerations of three objects:
Question
Mechanics Lecture 16, Slide 24
T1
T2
R
m1
m3
FGRAV
m2A) a1 > a2 >a3
B) a1 = a2 = a3
C) a1 = ra2 = a3
D) a1 = a2/r= a3
Two blocks connected by strings which is looped over a pulley of mass m2 and radius r. The pulley turns on a frictionless axle but there is friction between the string and the pulley. m1 sits on a frictionless table and m3 is acted by the force of gravity Fgrav.
Compare the magnitudes of the force of gravity and the tension in the strings:
Question
Mechanics Lecture 16, Slide 25
T1
T2
R
m1
m3
A) FGRAV > T2 >T1
B) FGRAV = T2 = T1
C) FGRAV > T2 =T1
D) FGRAV = T2 >T1
FGRAV
m2
A force F is applied to a disk which sits on a frictionless
surface for a time interval t in two ways.
• In (A) it is applied to a string tied to the center of the disk.
• In (B) it is applied to a string wrapped around the disk.
In which case does the disk acquire the greater center-of-
mass speed after 2 seconds?
Question
Mechanics Lecture 16, Slide 26
F
R
a) A
b) B
c) They both acquire the same COM speed
d) Depends on the mass of the disk
F(A)
(B)
Top View
A force F is applied to a disk which sits on a frictionless surface
for a time interval t in two ways.
• In (A) it is applied to a string tied to the center of the disk.
• In (B) it is applied to a string wrapped around the disk.
In which case does the disk acquire the greater total kinetic
energy after 2 seconds?
Question
Mechanics Lecture 16, Slide 27
F
R
F(A)
(B)
a) A
b) B
c) They both acquire the same energy
d) Depends on the mass of the disk
Top View
Example 16.5 (bowling ball)
A spherical bowling ball with mass m = 4.3 kg and radius R = 0.105 m is thrown down the lane with an initial translational speed of v = 8.5 m/s and no rotational speed. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.33. Once the ball begins to roll without slipping it moves with a constant velocity down the lane.
Mechanics Lecture 16, Slide 28
How long does it take the bowling ball to begin rolling without slipping?
Question
Mechanics Lecture 16, Slide 29
While it is moving down the bowling alley but still slipping, which of the following can we apply?
a)SF=macom
b) St=Iac) Both (a) and (b)d) Neither (a) or (b)e) Sometimes only (a) and then sometimes
only (b)
Question
Mechanics Lecture 16, Slide 30
As the ball skids on the alley, what can we say about the magnitudes of vcom and w?
a)|vcom|will increase, |w|will increaseb)|vcom|will decrease, |w|will decreasec) |vcom|will decrease, |w|will increased) |vcom|will increase, |w|will decreasee) |vcom|will decrease, |w|will remain constant
Question
Mechanics Lecture 16, Slide 31
How we will know when the ball is rolling without slipping?
a) It’s when w*r = vcom
b) It’s when a*r = atan
c) It’s when vtan = 0d) It’s when vcom = 0e) It’s when KErot = KEtran