Explanation Given data: Refer to the Example 96.11 in the textbook for required data to obtain the objective. The radius of the merry-go-round ( r ) is 2 m. Mass of the merry-go-round ( m M ) is 200 kg. Initial angular speed of the merry-go-round ( ω M ) i is 0 rad s since the merry-go-round is initially at rest. Initial angular velocity of the Joe ( ω J ) i is 0 rad s since the Joe is also initially at rest. Final velocity of the Joe ( v J ) f is 5.0 m s . Mass of the Joe ( m J ) is 36 kg. Formula used: Write the expression for angular momentum of conservation for two particles. ( I 1 ) i ( ω 1 ) i + ( I 2 ) i ( ω 2 ) i = ( I 1 ) f ( ω 1 ) f + ( I 2 ) f ( ω 2 ) f (1) Here, ( I 1 ) i is the initial moment of inertia of first particle, ( I 2 ) i is the initial moment of inertia of second particle, ( I 1 ) f the final moment of inertia of first particle, ( I 2 ) f is the final moment of inertia of second particle, ( ω 1 ) i is the initial angular speed of the first particle, ( ω 2 ) i is the initial angular speed of the second particle, ( ω 1 ) f is the final angular speed of the first particle, and ( ω 2 ) f is the final angular speed of the second particle. Write the expression for moment of inertia of rotating particle (disk). I = 1 2 m r 2 (2) Here, m is the mass of a particle, and r is the radius of motion of the particle. Write the expression for moment of a particle that jumps on the rotating particle. I = m r 2 (3) Here, m is the mass of the particle, and r is the radius of motion of the rotating particle. Write the expression for the angular velocity of the particle as follows. ω = v r (4) Here, v is the velocity of a particle. Explanation: Consider merry-go-round and Joe as isolated systems. As there are no external forces, the angular momentum of the system is conserved for the given system. Modify equation (1) for the given system as follows. ( I M ) i ( ω M ) i + ( I J ) i ( ω J ) i = ( I M ) f ( ω M ) f + ( I J ) f ( ω J ) f Here, ( ω M ) f is the final angular speed of the merry-go-round, and ( ω J ) f is the final angular speed of the Joe. Rearrange the expression to find the final angular speed of the merry-go-round. ( I M ) f ( ω M ) f = ( I M ) i ( ω M ) i + ( I J ) i ( ω J ) i − ( I J ) f ( ω J ) f ( ω M ) f = ( I M ) i ( ω M ) i + ( I J ) i ( ω J ) i − ( I J ) f ( ω J ) f ( I M ) f (5) The moment of inertia is constant (same) in both the states (initial and final states) Calculation of moment of inertia for merry-go-round: Substitute 200 kg for m , and 2 m for r in equation (2)

College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

4th Edition

ISBN: 9780134641492

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 9, Problem 77GP

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To find: The final angular speed of the merry-go-round.

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Chapter 9, Problem 76GP

Chapter 9, Problem 78GP

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College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

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Ch. 9 - You probably know that it feels better to catch a...Ch. 9 - In the early days of rocketry, some people claimed...Ch. 9 - Two ice skaters, Megan and Jason, push off from...Ch. 9 - Suppose a rubber ball and a steel ball collide....Ch. 9 - While standing still on a basketball court, you...Ch. 9 - To win a prize at the county fair, youre trying to...Ch. 9 - Monica stands at the edge of a circular platform...Ch. 9 - If the earth warms significantly, the polar ice...Ch. 9 - Prob. 21CQ Ch. 9 - Prob. 23MCQ Ch. 9 - Curling is a sport played with 20 kg stones that...Ch. 9 - Prob. 25MCQ Ch. 9 - Prob. 26MCQ Ch. 9 - Prob. 27MCQ Ch. 9 - A 4.0-m-diameter playground merry-go-round, with a...Ch. 9 - A disk rotates freely on a vertical axis with an...Ch. 9 - At what speed do a bicycle and its rider, with a...Ch. 9 - Prob. 2P Ch. 9 - A 57 g tennis ball is served at 45 m/s. If the...Ch. 9 - Prob. 4P Ch. 9 - A student throws a 120 g snowball at 7.5 m/s at...Ch. 9 - Prob. 6P Ch. 9 - Prob. 7P Ch. 9 - Prob. 8P Ch. 9 - Use the impulse-momentum theorem to find how long...Ch. 9 - Prob. 10P Ch. 9 - Prob. 11P Ch. 9 - Prob. 12P Ch. 9 - A child is sliding on a sled at 1.5 m/s to the...Ch. 9 - Prob. 14P Ch. 9 - As part of a safety investigation, two 1400 kg...Ch. 9 - In a Little League baseball game, the 145 g ball...Ch. 9 - Prob. 18P Ch. 9 - A small, 100 g cart is moving at 1.20 m/s on a...Ch. 9 - Prob. 20P Ch. 9 - A 2.7 kg block of wood sits on a frictionless...Ch. 9 - Prob. 22P Ch. 9 - A 10,000 kg railroad car is rolling at 2.00 m/s...Ch. 9 - Prob. 24P Ch. 9 - A 55 kg hunter, standing on frictionless ice,...Ch. 9 - Prob. 26P Ch. 9 - Prob. 27P Ch. 9 - Prob. 28P Ch. 9 - A 71 kg baseball player jumps straight up to catch...Ch. 9 - Prob. 30P Ch. 9 - A kid at the junior high cafeteria wants to propel...Ch. 9 - The parking brake on a 2000 kg Cadillac has...Ch. 9 - A 2.0 kg block slides along a frictionless surface...Ch. 9 - Erica (36 kg) and Danny (47 kg) are bouncing on a...Ch. 9 - A 20 g ball of clay traveling east at 3.0 m/s...Ch. 9 - Prob. 37P Ch. 9 - A 20 g ball of clay traveling east at 2.0 m/s...Ch. 9 - A firecracker in a coconut blows the coconut into...Ch. 9 - Prob. 40P Ch. 9 - Prob. 41P Ch. 9 - Divers change their body position in midair while...Ch. 9 - Prob. 43P Ch. 9 - What is the angular momentum of the moon around...Ch. 9 - Prob. 46GP Ch. 9 - Prob. 47GP Ch. 9 - Prob. 48GP Ch. 9 - Prob. 49GP Ch. 9 - Prob. 50GP Ch. 9 - Prob. 51GP Ch. 9 - A 140 g baseball is moving horizontally to the...Ch. 9 - A tennis player swings her 1000 g racket with a...Ch. 9 - A 20 g ball of clay is thrown horizontally at 30...Ch. 9 - Dan is gliding on his skateboard at 4.0 m/s. He...Ch. 9 - Ethan, whose mass is 80 kg, stands at one end of a...Ch. 9 - Three identical train cars, coupled together, are...Ch. 9 - A 110 kg linebacker running at 2.0 m/s and an 82...Ch. 9 - Most geologists believe that the dinosaurs became...Ch. 9 - Two ice skaters, with masses of 75 kg and 55 kg,...Ch. 9 - Prob. 62GP Ch. 9 - One billiard ball is shot east at 2.00 m/s. A...Ch. 9 - A 10 g bullet is fired into a 10 kg wood block...Ch. 9 - A typical raindrop is much more massive than a...Ch. 9 - A 15 g bullet is fired at 610 m/s into a 4.0 kg...Ch. 9 - Prob. 67GP Ch. 9 - Two 500 g blocks of wood are 2.0 m apart on a...Ch. 9 - A spaceship of mass 2.0 106 kg is cruising at a...Ch. 9 - At the county fair, Chris throws a 0.15 kg...Ch. 9 - Prob. 73GP Ch. 9 - The carbon isotope 14C is used for carbon dating...Ch. 9 - Prob. 75GP Ch. 9 - A 2.0 kg, 20-cm-diameter turntable rotates at 100...Ch. 9 - Prob. 77GP Ch. 9 - A 3.0-m-diameter merry-go-round with a mass of 250...Ch. 9 - Disk A, with a mass of 2.0 kg and a radius of 40...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...

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