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Announcements

Announcements. Read Chapter 8. CAPA assignment #10 is due Friday at 10 PM. Recitation Review 1: required. Chs . 1-7. Print & bring to class . . Lab make-up : Labs 1 - 3 . - at least 5 labs are required to pass the course;

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Announcements

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  1. Announcements • Read Chapter 8. • CAPA assignment #10 is due Friday at 10 PM. • Recitation Review 1:required. Chs. 1-7. Print & bring to class. • 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.

  2. Motion of a “rigid” body about a fixed axis of rotation. Rotational Motion Conservation of mechanical energy NII for rotations Conservation of angular momentum

  3. Motion of a “rigid” body about a fixed axis of rotation. Rotational Motion angle of rotation (rads) polar coordinates

  4. Motion of a “rigid” body about a fixed axis of rotation. Rotational Motion angular velocity (rad/s)

  5. Motion of a “rigid” body about a fixed axis of rotation. Rotational Motion angular acceleration (rad/s2)

  6. Rotational Kinematics Remember: s = r θ (θ: rads) (r,θ) polar coordinates For circular motion, θcompletely describes the motion. It gives the “rotational position”. Circumference: C = 2πr 360° = 2π rad 180° = π rad 57.3° = 1 rad

  7. Rotational Kinematics arc-length formula s = rθ Δs tangential velocity (m/s) use arc-length formula r = const for circular motion define: angular velocity ω Rate at which θ is changing

  8. Clicker Question Room Frequency BA A pocket watch and Big Ben are both keeping perfect time. Which minute hand has larger angular velocity ω? Pocket watch. Big Ben. Same ω.

  9. 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? Pocket watch. Big Ben. Same v. v = rω

  10. 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? vS = vL vS > vL vS < vL

  11. 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? ωS = ωL ωS > ωL ωS < ωL

  12. Rotational Kinematics arc-length formula s = rθ angular velocity Δs Units: Note: rpm = 60 f= 60/τ

  13. Rotational Kinematics s = r θ arc-length formula Rate at which θ is changing Δs tangential acceleration (m/s2) use equation for ω r = const for circular motion define: angular acceleration α Rate at which ω is changing

  14. Clicker Question Room Frequency BA 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.

  15. 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

  16. Clicker Question Room Frequency BA s = r θ A vinyl record has radius r = 6 in = 15.2 cm and spins at 33.3 rpm (revolutions per minute). What is its period? 33.3 sec B) 3 sec C) 1.8 sec D) 0.55 sec

  17. Clicker Question Room Frequency BA s = rθ 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? 33.3 Hz B) 3 Hz C) 1.8 Hz D) 0.55 Hz

  18. Clicker Question Room Frequency BA s = r θ 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? 0.55 Hz B) 3.49 rad/sec C) 1.8 rad/sec D) 0.88 rad/sec

  19. Clicker Question Room Frequency BA s = rθ 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? 53 cm/sec B) 3.49 cm/sec C) 4.35 cm/sec D) 8.44 cm/sec

  20. Clicker Question Room Frequency BA s = r θ 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/s2C) 53 cm/s2D) 0 cm/s2

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