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)

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summary so far


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


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.


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)


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


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

+


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

+


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+


=

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?


2m

1m

Question


Which of the following best represents the FBD of the cylinder as it’s rolling down the ramp?

(A) (B) (C) (D) (E)

Question


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)




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




2m

1m

CheckPoint


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


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:


Question


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


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


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


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


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


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


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


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.


How long does it take the bowling ball to begin rolling without slipping?

Question


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


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

physics 2111 unit 16 - college of dupage · physics 2111 unit 16 today’s concepts: a) work and ke...

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