ANNOUNCEMENTS

• Lab make-up: Labs 1 - 3.

- at least 5 labs are required to pass the course;- contact your TA to arrange lab makeup ahead of time. You will need to attend twice: (1) for lab make-up; and (2) for review recitation. You can attend any other section (in addition to your regular section), with that section’s TA advance permission.

• Read Chapter 8.

• CAPA assignment #10 is due Friday at 10 PM.

• Recitation Review 1: required. Chs. 1-7. Print & bring to class.

Rotational Motion

atan

r

v

r

NII for rotations

Fnett p nett L Conservation of angular momentum

KE PE constant KEtrans KErot PE constant

Conservation of mechanical energy

Motion of a “rigid” body about a fixed axis of rotation.

Rotational Motion

polar coordinates

angle of rotation (rads)

Motion of a “rigid” body about a fixed axis of rotation.

Rotational Motion

angular velocity (rad/s)

Motion of a “rigid” body about a fixed axis of rotation.

Rotational Motion

atan

r

v

r

angular acceleration (rad/s2)

Motion of a “rigid” body about a fixed axis of rotation.

Rotational Kinematics

Remember: s = r θ

(r,θ) polar coordinates

For circular motion, θ completely describes the motion. It gives the “rotational position”.

(θ: rads)

Circumference: C = 2πr 360° = 2π rad 180° = π rad

57.3° = 1 rad

s = r θ

v st

(r )

t

rt

r

t

v

r

tangential velocity (m/s)

arc-length formula

use arc-length formula

r = const for circular motion

define: angular velocity ω

Δs

Rate at which θ is changing

Rotational Kinematics

A pocket watch and Big Ben are both keeping perfect time. Which minute hand has larger angular velocity ω?

A) Pocket watch.

B) Big Ben.

C) Same ω.

Clicker Question Room Frequency BA

A pocket watch and Big Ben are both keeping perfect time. Which minute hand’s tip has larger tangential velocity v?

A) Pocket watch.

B) Big Ben.

C) Same v.

v = rω

Clicker Question Room Frequency BA

A small wheel and a large wheel are connected by a belt. The small wheel turns at a constant angular velocity ωS.

There is a bug S on the rim of the small wheel and a bug L on the rim of the big wheel. How do their speeds compare?

A) vS = vL

B) vS > vL

C) vS < vL

Clicker Question Room Frequency BA

A small wheel and a large wheel are connected by a belt. The small wheel turns at a constant angular velocity ωS.

How does the magnitude of the angular velocity of the large wheel ωL compare to that of the small wheel ωS?

A) ωS = ωL

B) ωS > ωL

C) ωS < ωL

Clicker Question Room Frequency BA

s = r θ

t

v

r

arc-length formula

Δs angular velocity

Units:

f # revolutions

sec

1 rev

period

1

(Hz)

# radians

sec

2period

2

2 f

v r 2r

2rf

Note: rpm = 60 f = 60/τ

Rotational Kinematics

Rotational Kinematics s = r θ t

v

rarc-length formula

Δs

Rate at which θ is changing

ar is due to change in direction of

velocity vector v (centripetal accel)

atan is due to change in the magnitude

(speed) of v

| a

| a atan2 ar

2

atan vt

(r )

t

rt

r

t

atan

r

tangential acceleration (m/s2)

use equation for ω

r = const for circular motion

define: angular acceleration α

Rate at which ω is changing

A ladybug is clinging to the rim of a wheel spinning CCW.

Assuming that the wheel is spinning at a constant rate, what is the direction of her acceleration when she’s at the far right?

Since her speed is constant, atan = 0, so the only acceleration is centripetal acceleration pointing toward the center of the wheel.

Clicker Question Room Frequency BA

A ladybug is clinging to the rim of a wheel spinning CCW.

Assuming that the wheel is speeding up, what is the direction of her acceleration when she’s at the far right?

v2 > v1

Clicker Question Room Frequency BA

A vinyl record has radius r = 6 in = 15.2 cm and spins at 33.3 rpm(revolutions per minute).

What is its period?

A) 33.3 sec B) 3 sec

C) 1.8 sec D) 0.55 sec

33.3 rev

1 min

1 min

33.3 rev

60sec

1min

1.8

sec

rev

s = r θ

t

v

r

2

2 f

t

atan

r

Clicker Question Room Frequency BA

A vinyl record has radius r = 6 in = 15.2 cm and spins at 33.3 rpm (revolutions per minute).

1. What is its period?

2. What is its frequency?

A) 33.3 Hz B) 3 Hz

C) 1.8 Hz D) 0.55 Hz

f 1 / 1

1.8sec0.55 Hz

s = r θ

t

v

r

2

2 f

t

atan

r

Clicker Question Room Frequency BA

1.8sec

A vinyl record has radius r = 6 in = 15.2 cm and spins at 33.3 rpm (revolutions per minute).

1. What is its period?

2. What is its frequency?

3. What is its angular velocity?

A) 0.55 Hz B) 3.49 rad/sec

C) 1.8 rad/sec D) 0.88 rad/sec

f 0.55 Hz

2 f (2)(3.14)(0.55) rad / sec 3.49 rad / sec

s = r θ

t

v

r

2

2 f

t

atan

r

1.8sec

Clicker Question Room Frequency BA

A vinyl record has radius r = 6 in = 15.2 cm and spins at 33.3 rpm (revolutions per minute).

1. What is its period?

2. What is its frequency?

3. What is its angular velocity?

4. What is the speed v of a bug on its rim?

A) 53 cm/sec B) 3.49 cm/sec

C) 4.35 cm/sec D) 8.44 cm/secv r (15.2cm)(3.49 rad / sec)

= 53.0 cm / sec

s = r θ

t

v

r

2

2 f

t

atan

rf 0.55 Hz

1.8sec

3.49 rad / sec

Clicker Question Room Frequency BA

A vinyl record has radius r = 6 in = 15.2 cm and spins at 33.3 rpm (revolutions per minute).

1. What is its period?

2. What is its frequency?

3. What is its angular velocity?

4. What is the speed v of a bug on its rim?

5. What is the magnitude of the acceleration of the bug?

A) 184 cm/s2 B) 103 cm/s2 C) 53 cm/s2 D) 0 cm/s2

constant 0 ar v2

r

(53cm / s)2

15.2cm184cm / s2

atan r 0 1.84m / s2 0.2g

s = r θ

t

v

r

2

2 f

t

atan

r

v 53.0 cm / sec

Clicker Question Room Frequency BA

1.8sec

f 0.55 Hz

3.49 rad / sec