Chapter 11. Rotation of Rigid Bodies

Uniform Angular Acceleration
11-1. A cable is wrapped around a drum 80 cm in diameter. How many revolutions of this drum will cause an object attached to the cable to move a linear distance of 2 m? What is the angular displacement? [ R = 0.04 m, s = 2 m, ( = ? ] [pic] = 5 rad [pic]; ( = 0.796 rev

11-2. A bicycle wheel is 26 in. in diameter. If the wheel makes 60 revolutions, what linear distance will it travel? [ D = 26 in.; R = 13 in. = 1.083 ft ]
[pic]; s = (R = (377 rad)(1.083 ft); s = 408 ft

11-3. A point on the edge of a large wheel of radius 3 m moves through an angle of 370. Find the length of the arc described by the point.
[pic]; s = …ver más…

(Cont.) The final angular speed is twice the average since ωo = 0: ωf = 8.38 rad/s vf = ωfR = (8.38 rad/s)(0.15 m); vf = 1.26 m/s

11-9. A cylindrical piece of stock 6 in. in diameter rotates in a lathe at 800 rpm. What is the linear velocity at the surface of the cylinder? [ R = D/2 = 3 in. = 0.250 ft ]
[pic]; v = 20.9 ft/s

11-10. The proper tangential velocity for machining steel stock is about 70 cm/s. At what rpm should a steel cylinder 8 cm in diameter be turned in a lathe? R = (0.08 m/2) = 0.04 m
[pic]; [pic];
[pic]; f = 0.279 rev/s(60 s/min); f = 16.7 rpm
11-11. For the wheel in Problem 11-8, what is the angular acceleration? What is the linear acceleration of a point on the edge of the wheel? [ ωf = 8.38 rad/s; ωo = 0, t = 3 s ]
[pic]; α = 2.79 rad/s2 a = αR = (2.79 rad/s2)(0.15 m); a = 0.419 m/s2
11-12. A circular drum of radius 40 cm is initially rotating at 400 rpm. It is brought to a stop after making 50 revolutions. What was the angular acceleration and the stopping time?
2αθ ’ ωf2 - ωo2; ( = 50 rev(2( rad/rev) = 314 rad; f = 400 rpm = 41.9 rad/s
[pic]; α = 2.79 rad/s2
[pic]; t = 15.0 s
11-13. A belt is wrapped around the edge of a pulley that is 40 cm in diameter. The pulley rotates with a constant angular acceleration of 3.50 rad/s2. At t = 0, the rotational speed is 2 rad/s. What is the angular displacement and angular velocity of the pulley 2 s later? θ ’ ω0t +