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Examples in Chapter 9

Examples in Chapter 9 . 9.25. A flywheel with a radius of 0.3 m starts from rest and accelerates with a constant angular acceleration of 0.6 rad/s 2 . Compute the magnitude of the angular accleration the radial acceleration The resultant acceleration of a point on its rim At the start

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Examples in Chapter 9

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  1. Examples in Chapter 9

  2. 9.25 • A flywheel with a radius of 0.3 m starts from rest and accelerates with a constant angular acceleration of 0.6 rad/s2 . Compute the magnitude of • the angular accleration • the radial acceleration • The resultant acceleration of a point on its rim • At the start • After it has turned through 600 • After it has turned through 1200

  3. Starting conditions • a = 0.3 rad/s • w0 =0 • r= 0.3 m

  4. Equations to think about

  5. At the start

  6. At 600

  7. At 1200

  8. 9.46 • A light flexible rope is wrapped several times around a hollow cylinder with a weight of 40 N and a radius of 0.25 m that rotates without friction about a fixed horizontal axis. The cylinder is attached is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 5 m at which the end of the rope is moving at 6 m/s. If the rope does not slip on the cylinder, what is the value of P?

  9. Some figurin’ • W=DR • Where R= ½ I w2 • v=rw or v/r=w • Initially, w0 =0 so DR= ½ I (v/r)2 • From I=m*r2=(40 N/9.8)*(.25)2=0.255 • W=F*d or P*(5 m) • W=5P • P= (1/2)*0.255*(6/.25)2/5=14.7 N

  10. 9.71 • A vacuum cleaner belt is looped over a shaft of radius 0.45 cm and a wheel of radius 2.0 cm . The arrangement is shown below. The motor turns the shaft at 60 rev/s and the shaft is connected to a beater bar which sweeps the carpet. Assume that the belt doesn’t slip. • What is the speed of a point on the belt? • What is the angular velocity of the belt?

  11. Some more figurin’ • Part a) v=r*w where • r=0.45 cm • w= 60 rev/s *(2*p radians/rev)=377 rad/s • v=0.45*377=169 cm/s or 1.69 m/s • Part b) w2= 169 cm/s / 2 cm =84.8 rad/s

  12. Hint on 9.72 • The wheels are coupled so that there is the tangential velocity is constant so that w1/w2 = r2/r1

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