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4. Ship's Propeller Problem The propellers on an average freighter have a radius of 4 ft (Figure 4-4e). At full speed ahead, the propellers turn at 150-rpm. a. What is the angular velocity in radians per minute at the tip of the blades? at the center of the propeller? What is the linear velocity in feet per minute at the tip of the blades? at the center of the propeller? b. Lawn Mower Blade Problem In order for a lawn mower blade (Figure 4-4f) to cut grass, it must strike the grass with a speed of at least 900 in/s. a. If the innermost part of the cutting edge is 6 in. from the center of the blade, how many radians per second must the blade turn? How many revolutions per minute is this? b. The blade has a diameter of 19 in. If the outermost tip of the blade hits a rock while turning as in part (a), how fast could the rock be hurled from the mower? t-61l~ O~ 19" 5. ~ ',}gure 4-4e 2. Ferris WheeL Problem Dan Druff and Ella Funt are riding on a Ferris wheel. Dan observes that it takes 20 s to make a complete revolution. Their seat is 25 ft from the axle· of the wheel. a. b. 3. -~ ) _ .\ Lawn Mower Cord Problem Yank Hardy pulls the cord on his power mower. In order for the engine to start, the pulley must turn at 180 revolutions per minute. The pulley has a radius of 0.2 ft (Figure 4-4g). a. How many radians per second must the pulley turn? b, How fast must Yank pull the cord to start the mower? c. When Yank pulls this hard, what is the angular velocity of the center of the pulley? What is their angular velocity in revolutions per minute? degrees per minute? radians per minute? What is their linear velocity? David and Goliath Problem David puts a rock in his sling and starts whirling it around. He realizes that in order for the rock to reach Goliath, it must leave the sling at a speed of 60 ftls. So he swings the sling in a circular path of radius 4 ft. What must the angular velocity be in order for David to achieve his objective? 6. Cockroach Problem A cockroach is sitting 4 em from the center of a Lazy Susan. Unaware of its presence, Phoebe Small spins the Lazy Susan through an angle of 120°. a. Through how many radians did the roach turn? b. What distance did it travel? c. If Phoebe turned the Lazy Susan 1200 in 4 second, what was the roach's angular velocity? d. What was its linear velocity? + '0 oi- h a.. .b) +~\ f - \ J.. 0 0 11 f!. + C~n-\.Q.t - 15 r~ '1. ct.) \ S0 S. 0...) c..) b) e f) 0 Cl.d /s e.. c. ~ """" 1'-1 3 ~ In Ise..c ~rr rQ.4/Sec C.) ,-. f" 14J.5 b) Cl (. 4/ S eo c. 3. b) / rt\"J f l I,;).. ---IT r...- ~rr -3 <glT -3 3,77 r4cl / £ e C ~17 C I"r\ • C) 411 ~ ~ rt:t4 Isec . 4) ¥ (rn /Sc.c F-+}se.c r(, 1/ I t1'"\ '( n .s