HW5
Rs1. 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, = ? ]
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 ]
3. An electric motor turns at 600 rpm. What is the angular velocity? What is the angular displacement after 6 s?
4. 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 ]
5. 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
6. 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?
7. A grinding disk is brought to a stop in 40 rev. If the braking acceleration was –6 rad/s2, what was the initial frequency or revolution in rev/s? [ = 40 rev (2) = 251 rad ]
8. A 2-kg mass and a 6-kg mass are connected by a light 30-cm bar. The system is then rotated horizontally at 300 rpm about an axis 10 cm from the 6-kg mass. What is the moment of inertia about this axis? What is the rotational kinetic energy?
6 kg2 kg20 cm10 cm
9. A 1.2-kg bicycle wheel has a radius of 70 cm with spokes of negligible weight. If it starts from rest and receives an angular acceleration of 3 rad/s2, what will be its rotational kinetic energy after 4 s? (The bicycle wheel approximates a circular hoop.
10. What is the input work of a 30 percent efficient gasoline engine if during each cycle it performs 400 J of useful work?
11. A 60-W motor…