When the ball reaches the break in the circle, which …...For uniform circular motion, the...

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When the ball reaches the break in the

circle, which path will it follow?

Checking Understanding:

Circular Motion Dynamics

Slide 6-21


Answer

When the ball reaches the break in the

circle, which path will it follow?

C.

Slide 6-22


A coin sits on a rotating

turntable.

At the time shown in

the figure, which arrow

gives the direction of

the coin’s velocity?

Additional Questions

Slide 6-45


Answer: A

A coin sits on a

rotating turntable.


the figure, which arrow

gives the direction of

the coin’s velocity?

A

Slide 6-46


A coin sits on a

rotating turntable.

At the instant shown,

suppose the frictional

force disappeared. In

what direction would

the coin move?


Slide 6-49


Answer

A

A coin sits on a

rotating turntable.

At the instant shown,

suppose the frictional

force disappeared. In

what direction would

the coin move?

Slide 6-50


When a ball on the end of a string is swung

in a vertical circle, the ball is accelerating

because

A. the speed is changing.

B. the direction is changing.

C. the speed and the direction are

changing.

D. the ball is not accelerating.

Checking Understanding

Slide 6-13


Answer


in a vertical circle, the ball is accelerating

because

A. the speed is changing.

B. the direction is changing.

C. the speed and the direction are

changing.

D. the ball is not accelerating.

Slide 6-14


For the ball on the end of a string moving in

a vertical circle:

What is the direction of the net force on the

ball?

A. tangent to the circle

B. toward the center of the circle

C. there is no net force



Slide 6-19


Answer


a vertical circle:

What is the direction of the net force on the

ball?

A. tangent to the circle

B. toward the center of the circle

C. there is no net force

Slide 6-20



a vertical circle:

What force is producing the centripetal

acceleration of the ball?

A. gravity

B. air resistance

C. normal force

D. tension in the string



Slide 6-17


Answer


a vertical circle:

What force is producing the centripetal

acceleration of the ball?

A. gravity

B. air resistance

C. normal force

D. tension in the string

Slide 6-18


A coin sits on a

rotating turntable.


the figure, which

arrow gives the

direction of the

frictional force on the

coin?


Slide 6-47


Answer

A coin sits on a

rotating turntable.


the figure, which

arrow gives the

direction of the

frictional force on the

coin?

D

Slide 6-48


Reading Quiz

For uniform circular motion, the acceleration

A. is parallel to the velocity.

B. is directed toward the center of the

circle.

C. is larger for a larger orbit at the same

speed.

D. is always due to gravity.

E. is always negative.

Slide 6-6


Answer

For uniform circular motion, the acceleration

A. is parallel to the velocity.

B. is directed toward the center of the

circle.

C. is larger for a larger orbit at the same

speed.

D. is always due to gravity.

E. is always negative.

Slide 6-7


Summary

Slide 6-41

Speed = v = Δd/Δt = 2πr/T

at radius, r,



in a vertical circle:

What is the direction of the acceleration of

the ball?

A. Tangent to the circle, in the direction

of the ball’s motion

B. Toward the center of the circle


Slide 6-15


Answer


in a vertical circle:

What is the direction of the acceleration of

the ball?

A. Tangent to the circle, in the direction

of the ball’s motion

B. Toward the center of the circle

Slide 6-16


Angular Displacement, , and Angular Velocity, ω

is the angle between position 1 and 2.

is the amount of rotation—measured in degrees or radians (we’ll use radians since they are the SI unit for ).

1

2

r

For an object rotating about a fixed axis, the angular displacement, , is the angle swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly. By convention, the angular displacement is positive if it is counterclockwise.


Angular Displacement,

For an object rotating, angular displacement is found by:

(in radians) = Arc length = s

= f – i where i is sometimes zero.

radius r


If determining for a complete circle, or one complete cycle:

Arc length = 2r (for one revolution)

= (arc length) / r

= (2r) / r = 2 radians

1 revolution = 2 radians = 360o

So, 1 radian = 360o / 2 = 57.3o


UNIFORM CIRCULAR MOTION (UCM)

Angular displacement = Δθ = the angle displaced, measured in radians, while an object undergoes UCM

Δθ= ω Δt

Angular Velocity = ω (Greek: Omega)

ω = 2 π f and ω = Δθ/Δt

All points on a rotating object rotate through the same angle in the same time, and have the same frequency. Angular velocity is also known as the turning rate.

Angular velocity: all points on a rotating object have the same angular velocity, ω, (same turning rate) but different speeds, v, and v =ωr, depending on the location of that point.

v =ωr


ω is positive if object is rotating counterclockwise. (Negative if rotation is clockwise.)

Conversion: 1 revolution = 2 π rad


Angular Velocity Angular Velocity = the “turning rate”—expressed in units of

revolutions per second, or metric: radians per second.

Angular velocity = angular displacement / elapsed time

= /t units: radians/second or rad/s

For one cycle: t = T = period = time for one cycle

And, =s/r= (2r)/r = 2 radians = angular

displacement for one cycle

= /t = 2 radians / T = 2 / T

= 2/T And since T=1/f , where f = frequency

= 2 / (1/f) = 2f

= 2f Angular velocity is sometimes called angular frequency!



Two coins rotate on a turntable. Coin B is twice as

far from the axis as coin A.

A. The angular velocity of A is twice that of B.

B. The angular velocity of A equals that of B.

C. The angular velocity of A is half that of B.

Slide 7-13


Answer

All points on the turntable rotate through the

same angle in the same time. ω = θ/ tAll points have the same period, therefore, all

points have the same frequency.

ω = 2 π f

Two coins rotate on a turntable. Coin B is

twice as far from the axis as coin A.

A. The angular velocity of A is twice

that of B.

B. The angular velocity of

A equals that of B.

C. The angular velocity of A is half

that of B.

Slide 7-14


Important to realize… Angular velocity, , or the “turning rate” is the same everywhere on the rotating body/object, b/c /t =2/T is the same.

But, instantaneous velocity, the velocity tangent to the circular path—called tangential velocity, vT– is greater for points (places) farther from the axis.

The magnitude of the tangential velocity is referred to as the tangential speed.

v=d/t = 2r/T = 2rf

vT= r

vT

VT

vT

vT




A. The speed of A is twice that of B.

B. The speed of A equals that of B.

C. The speed of A is half that of B.


Slide 7-15


Answer

Twice the radius means twice the speed, v.

Therefore, B moves with twice the speed of A.



A. The speed of A is twice that of B.

B. The speed of A equals that of B.

C. The speed, v, of A is

half that of B.

Slide 7-16

v rw=


Uniform Circular Motion

Slide 6-23

From:vT= r = 2 π r fac =

a = ac

v = vT


Circular MotionAnd v = 2πrf =

tangential speed or

speed at that place (at r)

a = ac

When the ball reaches the break in the circle, which …...For uniform circular motion, the...

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