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PHYSICS WORKSHEET ROTATIONAL MOTION A NAME: _______________________________ 1. A beetle standing on the edge of 12- inch 2 kg disk is whirling around at 33 1/3 rotations per minute. A. Compute the magnitude of the creature’s angular velocity. (there are 2.54 cm in an inch) ϴ=33.33 ω=? t = 60 s ϴ=33.33 x 2πrad = 209.31 rads 3.48 rad/s ω = ϴ/t ω = 209.31/60 = B. Compute the magnitude of the creature’s centripetal acceleration. d=12 in r = 6 in 1.85 m/s2 ac = r ω 2 r = 2.54 cm/in (6 in) = 15.2 cm =0 .152 m ac = (0.152 m) (3.48 rad/s)2 = 1.85 C. Neglecting the mass of the beetle, what is the rotational inertia of the disk? m = 2 kg I = mr2 I = 2 kg x (0.152 m)2 = 0.046 kgm2 D What is the angular momentum of the disk? L = Iω 2. L = (0.046 kgm2)( 3.48 rad/s) = 0.160 kg∙m2/s If a torque of 55.0 N∙m is required and the largest force that can be exerted by you is 135 N, what is the length of the lever arm that must be used? 0.407 m T =55 N∙m F = 135 N r=? T/F =r 55/135 = PHYSICS WORKSHEET ROTATIONAL MOTION B NAME: _______________________________ 1. What is the angular momentum of a 6 kg mass traveling with a speed of 6 m/s in a circle of radius of 12 m? 432 kg·m2/s 2. If the torque required to loosen a nut on a wheel has a magnitude of 40.0 N·m and the force exerted by a mechanic is 133 N, how far from the nut must the mechanic apply the force? 0.3 m 3. A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 ´ 10–2 kg·m2, and a radius of 0.10 m. If it rolls down the lane without slipping at an angular speed of 4.0 ´ 101 rad/s, what is its angular momentum? 1.1 kgm2/s 4. A figure skater with arms drawn in spins on the ice at a rate of 5.0 rad/s and has an angular momentum of 9.4 kg·m2/s. What is the skater’s rotational inertia . 1.875 kg•m2 Extra Credit Gerry, whose mass is 43 kg, sits 1.8 m from the center of a seesaw. Steve, whose mass is 52 kg wants to balance Gerry. How far from the center of the seesaw should Steve sit? 1.5 m