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/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

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

Equations to think about

At the start

At 600

At 1200

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?

Some figurin’ W=DR v=rw or v/r=w Initially, w0 =0 so DR= ½ I (v/r)2 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

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?

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

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