A series of object are being rotated. The same net torque is being applied to ea

Question

A series of object are being rotated. The same net torque is being applied to each object. Rank the object in order of the resulting angular acceleration (1=lowest). A solid disk spinning about its center. Total mass is 0.5M and the radius is 2R. An object consisting of two objects connected by a massless rod. Each object has a mass of 2M and is a distance R from the axis of rotation. A solid disk spinning about its center. Total mass is M and a radius of R. A hoop spinning about its center. Total mass is 2M and a radius of R.

Explanation / Answer

Relation between torque( ) and angular acceleration () is torque, = I angular acceleration, = / I Here, net torque, is same .Therefore, angular acceleration is inversely proportional to moment of inertia. Relation between torque( ) and angular acceleration () is torque, = I angular acceleration, = / I Here, net torque, is same .Therefore, angular acceleration is inversely proportional to moment of inertia. Here, net torque, is same .Therefore, angular acceleration is inversely proportional to moment of inertia. _________________________________________________________________________ Given that, Mass , m = 0.5 M radius, r = R Moment of inertia for a solid sphere spinning about its center is, I = (2 / 5)mr2 = (2 / 5)(0.5 M)R2 = 0.2 MR2 Rank - 1 Rank - 1 ________________________________________________________________________ Mass of each object, m = 2 M distance, r = R Moment of inertia, I = mr2 + mr2 = 2mr2 = 2(2 M)R2 = 4MR2 Rank - 4 Rank - 4 _________________________________________________________________________ Mass, m = M radius, r = R Moment of inertia of a solid disk spinning about its cenrer is, I = (1/2)mr2 = (0.5)( 0.5 M)(2R)2 = MR2 Rank - 3 _________________________________________________________________________ Rank - 3 _________________________________________________________________________ Mass, m = 0.5 M radius, r = 2R Moment of inertia of a solid disk spinning about its cenrer is, I = (1/2)mr2 = (0.5)( M)(R)2 = 0.5 MR2 Rank - 2 Rank - 2   

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