A rod of length 80.0-cm has two small spheres attached to it, one at each end. The rod has negligible mass, but each of the two small spheres has a mass of 100-g. Calculate the rotational inertia of the system about an axis through the center of the rod. Calculate the rotational inertia of the system about an axis through the center of one sphere at the end of the rod.

A 250-g mass hangs from a string that is wrapped around a pulley, as shown in the figure. The pulley is suspended in such a way that it can rotate freely. When the mass is released, it accelerates toward the floor as the string unwinds. Model the pulley as a uniform solid cylinder of mass 1.00 kg and radius 9.00 cm. Assume that the thread has negligible mass and does not slip or stretch as it unwinds. Determine the magnitude a of the pulley's angular acceleration. rad/s? a = Determine the magnitude of the acceleration a of the descending weight. a = m/s? Calculate the magnitude of the tension T' in the string. T =

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The moment of inertia of an object about a certain axis is 1.2 kg-m2. Initially the object is at rest, and then it is accelerated at a constant rate of 25 rad-s-2. Determine the time required for the object to achieve a rotational kinetic energy of 1.50 kJ.

A uniform solid sphere of mass 12.0 kg and radius 7.0 cm rotates at 300 revolutions per minute (rpm) on an axis passing through its center. Calculate: a) Its moment of inertia b) Its rotational kinetic energy c) The angular momentum (L), that is, the magnitude of the product Iw, in the appropriate IS units d) Based on the general definition of the moment of inertia (I = Mr²), determine the radius of gyration of the sphere around the axis that passes through its center.

What is the angular acceleration and how long will it take to decrease rotational speed by 27 rad/s?

A person of mass 79 kg stands at the center of a rotating merry-go-round platform of radius 2.8 m and moment of inertia 890 kg⋅m2. The platform rotates without friction with angular velocity 0.95 rad/s. The person walks radially to the edge of the platform. Calculate the angular velocity when the person reaches the edge then calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk. Express your answers using three significant figures. For the second half, use two significant figures and enter your answers numerically separated by a comma.

A wheel has a radius of 0.1m and a moment of inertia of 4.00 kg-m2 starts from rest and accelerates under a constant torque of 12.0 N-m for 4.00 s. a) What is the wheel’s rotational kinetic energy at the end of 4.00 s? b) How far has the wheel rolled at the end of 4.00s?