Chapter 10. Uniform Circular Motion

Centripetal Acceleration
10-1. A ball is attached to the end of a 1.5 m string and it swings in a circle with a constant speed of 8 m/s. What is the centripetal acceleration?
[pic] ac = 42.7 m/s2

10-2. What are the period and frequency of rotation for the ball in Problem 10-1?
[pic]; T = 1.18 s
[pic]; f = 0.849 rev/s

10-3. A drive pulley 6-cm in diameter is set to rotate at 9 rev/s. What is the centripetal acceleration of a point on the edge of the pulley? What would be the linear speed of a belt around the pulley? [ R = (0.06 m/2) = 0.03 m ]
[pic]; ac = 95.9 m/s2 [pic]; v = 1.70 m/s

10-4. An object revolves in a …ver más…

(Slipping occurs when the centripetal force equals the maximum force of static friction.)
[pic];
f = 0.182 rev/s (60 s/min); f = 10.9 rpm

*10-19. A platform rotates freely at 100 rpm. If the coefficient of static friction is 0.5, how far from the center of the platform can a bolt be placed to without slipping? f = 100 rev/min (1 min/60 s) = 1.67 rev/s; (s = 0.5; R = ?
[pic]; R = 21.1 cm

10-20. Find the required banking angle to negotiate the curve of Prob.10-15 without slipping.
[pic]; ( = 21.80

10-21. Find the required banking angle for Problem 10-16 to prevent slipping?
[pic]; ( = 31.20

10-22. The optimum banking angle for a curve of radius 20 m is found to be 280. For what speed was this angle designed?
[pic]; v = 10.3 m/s
*10-23. A curve in a road 9 m wide has a radius of 96 m. How much higher than the inside edge should the outside edge be for an automobile to travel at the optimum speed of 40 km/h? v = 40 km/h = 11.1 m/s; h = (9 m) sin (; [pic]
[pic]; ( = 7.480; h = (9 m) sin 7.480; h = 1.17 m

The Conical Pendulum
10-24. A conical pendulum swings in a horizontal circle of radius 30 cm. What angle does the supporting cord make with the vertical when the liner speed of the mass is 12 m/s?
[pic]; ( = 88.80

10-25. What is the linear speed of the flyweights in Fig. 10-16 if L = 20 cm and ( = 600? What is the frequency of