Remember Newton’s 2nd Law?

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Remember Newton’s 2nd Law? For linear motion : F=ma a m F For rotational motion : =I I  

Example Treat the spindle as a solid cylinder. m = a) What is the moment of Inertia of the spindle? b) If the tension in the rope is 10 N, what is the angular acceleration of the wheel? c) What is the acceleration of the bucket? d) What is the mass M, of the bucket? m = M

Solution a) What is the moment of Inertia of the spindle? Given: m = 5 kg, r = 0.6 m M = 0.9 kgm2

Solution b) If the tension in the rope is 10 N, what is a? Given: I = 0.9 kg m2, T = 10 N, r = 0.6 m c) What is the acceleration of the bucket? Given: r=0.6 m, a = 6.67 rad/s M

Solution d) What is the mass of the bucket? Given: T = 10 N, a = 4 m/s2 M

1) A 1 kg wheel with a fixed hub start from rest, and a force is applied as shown. Assume that the hub and spokes are massless, and that F = 1 N, and the momentum of inertia is I = MR2. What is the magnitude of the wheel’s angular acceleration? M = 1 kg |F| = 1N R = 0.5 m Q = 60o w/r to horizontal ¼ rad/sec2 ½ rad/sec2 1 rad/sec2 2 rad/sec2 4 rad/sec2

2) A wheel (mass of 1kg and with a radius of 1m) with a fixed hub starts from rest, and forces are applied as shown. Assume that the hub and spokes are massless, and that the wheel is a hoop, I = MR2. F1 = 1 N and acts at a distance of half of the radius of the wheel. What is the angular acceleration of the wheel? F1=1N 1m 0.5m 0.25 rad/s2 0.50 rad/s2 1 rad/s2 2 rad/s2 4 rad/s2

3) Two identical wheels (mass of 1kg and with a radius of 1m) with fixed hubs start from rest, and forces are applied as shown. Assume that the hub and spokes are massless, and that F1 = 1 N. In order to impart identical angular accelerations, how large must F2 be? I = MR2 F1 F2 M = 1 kg 0.25 N 0.50 N 1 N 2 N 4 N F1 1m 0.5m

4) Two 1 kg wheels with fixed hubs start from rest, and forces are applied as shown. Assume that the hub and spokes are massless, and that F1 = 1 N. In order to impart identical angular accelerations, how large must F2 be? I = MR2 F1 F2 M = 1 kg R1 = 0.5 m R2 = 1.0 m 0.25 N 0.50 N 1 N 2 N 4 N

m Ex: A rotation and translation incline example Assume frictionless T Pulley: a disk mpulley = ? r = 0.20 m a=2.0 m/s2 2.0 kg m 20 a) Find the tension in the string. b) Find mass m. Treat the pulley as a solid cylinder. c) Find the torque on the pulley. d) Find the angular acceleration of the pulley. e) Find the rotational inertia of the pulley. f) Find the mass of the pulley.