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ANNOUNCEMENTS Lab make-up : Labs 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 Print & bring to class.

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

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

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

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Rotational Motion angular acceleration (rad/s 2 ) Motion of a “rigid” body about a fixed axis of rotation.

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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

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s = r θ 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

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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 QuestionRoom Frequency BA

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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 QuestionRoom Frequency BA

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A small wheel and a large wheel are connected by a belt. The small wheel turns at a constant angular velocity ω S. 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)v S = v L B)v S > v L C)v S < v L Clicker QuestionRoom Frequency BA

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A small wheel and a large wheel are connected by a belt. The small wheel turns at a constant angular velocity ω S. How does the magnitude of the angular velocity of the large wheel ω L compare to that of the small wheel ω S ? A)ω S = ω L B)ω S > ω L C)ω S < ω L Clicker QuestionRoom Frequency BA

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s = r θ arc-length formula Δs angular velocity Units : Note: rpm = 60 f = 60/τ Rotational Kinematics

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s = r θ arc-length formula Δs Rate at which θ is changing tangential acceleration (m/s 2 ) use equation for ω r = const for circular motion define: angular acceleration α Rate at which ω is changing

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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, a tan = 0, so the only acceleration is centripetal acceleration pointing toward the center of the wheel. Clicker QuestionRoom Frequency BA

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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? v 2 > v 1 Clicker QuestionRoom Frequency BA

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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 secB) 3 sec C) 1.8 secD) 0.55 sec s = r θ Clicker QuestionRoom Frequency BA

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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 HzB) 3 Hz C) 1.8 HzD) 0.55 Hz s = r θ Clicker QuestionRoom Frequency BA

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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 HzB) 3.49 rad/sec C) 1.8 rad/sec D) 0.88 rad/sec s = r θ Clicker QuestionRoom Frequency BA

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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/sec s = r θ Clicker QuestionRoom Frequency BA

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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/s 2 B) 103 cm/s 2 C) 53 cm/s 2 D) 0 cm/s 2 s = r θ Clicker QuestionRoom Frequency BA

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