23% 11: 09 AM LTE 1. Initially, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 3.0 rad/sec. Two seconds later it has turned through 5.0 complete revolutions. Find the angular acceleration 2. Given the position vector r= 3i + 4j +5k and force F = 16i - 20j - 5 k, find the magnitude of the torque vectort so that t = r x F ? (Hint: use 3x3 matrix) A solid disk of mass equal to 7.0 kg and radius of 30 cm changes its rotations gradually from 45 rpm to 120 rpm in 5.0 sec 3. find the angular acceleration in rad/s. 4. how many revolutions has the disk turned in this 5.0 seconds? 5. find the change in rotational kinetic energy 6. find its moment of inertia in kgm2 7. find the magnitude of torque needed to make such a change in rpm. 8. find the tangential acceleration of a point P on the outer rim of the disk. 20t2 The fan blade in a jet engine rotates from rest with the angular acceleration a = 9. find the angular velocity as a function of time. 10. find the angular displacement as a function of time. 11. if the rotational inertia of the blade is 5.0 kgm2, find the work done on the blade in the first initial 3.0 seconds. (Hint: take t from zero to 3 and d0 = odt) A hollow sphere ( M = 3.0 kg and R = 60 cm ) is rolling down an inclined surface with a height of 2.0 meters and an inclined angle of 25 degrees. 12. find the moment of inertia of the sphere, in kgm2 13. find the speed of the center of mass when it reaches the bottom of the hill 14. find the total rotational kinetic energy at the bottom h ך Ringtone 15. find the linear acceleration of the sphere, in m/sec2 16. for the sphere to make pure rotation, find the magnitude of the static frictional coefficient u ? A wheel (radius = 0.30 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object. When released from rest the object falls with a downward acceleration of 5.0 m/sec2 17. Find the tension on the cord. 18. Find the angular acceleration of the wheel T 19. Find the moment of inertia of the wheel mg A solid disk (M = 10 kg and R = 70 cm) is rotating at 300 rpm initially. Then a smaller ring ( m = 3.0 kg and r 40 cm ) is dropped concentrically onto the disk and they rotate together with a new angular velocity. (Hint: the rotational inertia of the small ring is mr, not /2 mr2!) 20. find the final angular velocity of the system in rpm. Y 21. find the change in rotational kinetic energy of the system. M 22. find the percent of energy loss during this collision between the solid disk and the ring A hollow spherical ball is let go from the top of a track and goes around a circular loop (R = 60 cm ). 23. What must be the minimum height of the track so that the ball will not fall off the track at the topmost point of the loop? R 24. When the above condition is met, what is the tangential speed of the ball when it reaches the topmost point? A 25-ft crane supported at its lower end by a pin is elevated by a horizontal cable. A 250-lb load is suspended through the cable. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. Hint: You don't have to convert the unit since they cancel out on both sides. 25. Find the tension in the cable 26. Find the total force acting on the pin. 60 250b W(260ib) לר