Question

Part I: The two wheels shown rotate about a fixed axle through their center (the masses and radii of the wheels are as shown in the diagram). The two wheels are initially at rest. A 1 N of force is applied to each wheel as shown. You can assume that the wheels are essentially hoops (Inoop = MR2). In order for F1 = 1N IF_1= 1 N the angular accelerations of the two wheels to be the same, at what angle must Fi be applied with respect to horizontal? (0.5 pt) M = 1 0 degrees kg b. 15 degrees R = 0.5 m c. 30 degrees d. 45 degrees R2 = 1.0 m e. 60 degrees f. 90 degrees a. M = 1 kg Part II: The wheel shown has radius R = 0.5 m and mass M = 1 kg. The wheel is essentially a hoop (Inoop = MR2). When a 1 N of force is applied at the angle shown, the wheel starts to spin about a fixed axis through its center. Calculate the magnitude of the wheel's angular acceleration about its axle. (0.5 pt) a. FI = 11 © = 60° wir to horizontal rad/s2 b. rad/s c. 1 rad/s2 d. 2 rad/s2 4 rad/s2 M = 1 kg R = 0.5 m Part III: The two wheels shown rotate about a fixed axle through their center (the masses and radii of the wheels are as shown in the diagram). The two wheels are initially at rest. You can assume that the wheels are essentially hoops (Ihoop = MR2). If F1 = 1 N, what should be the magnitude of Fz be in order for the two wheels to have the same magnitude of angular acceleration? (0.5 pt) M= 1 kg M 1 kg a. .25N b. 5 c. IN d. 2N 4N R = 0.5 m R = 1.0 m

Answer 1

Part 1 fa R7 Angular acceleration of the two wheels is same. ai - a2 T2 7 11 = FR2 FicoSOR MR? MR Ficos F2 Shoppe R R2 F2 R A = cos X F R2 A = cos -1 cos** (****) O = 60° Part II

a = a = Fcose MR2 a = (1) cos60 (1) * (0.5) 2 a = 2rad/s2 Part III Angular acceleration of the two wheels is same. 01 = 42 T1 T2 = 11 12 FR FR2 MR MR F alia R R R F2 RI F2 * (1) = 2N 0.5