The figure below represents a bicycle wheel comprised of a rim with a radius of R = 0.5 m and mass of M = 200 g, to which someone has added two m = 30 g sensors that are separated by an angle of 0 = 110°. The axis of rotation for the wheel is at its center, as represented by the vector symbol, for a direction into the page. m = 30 g R = 0.5 m M = 200 g m = 30 g a) Where is the center of mass of the wheel/sensor system? b) What is the rotational moment of inertia of the wheel/sensor system around its axis of rotation?

An electric fan is turned off, and its angular velocity decreases uniformly from 450 rev/min to 220 rev/min in a time interval of length 4.50s.  a) Find the angular acceleration α in revolutions per second per second.  b) Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A.  c) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A?

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller flywheel of radius 20 cm has a cord that has a pulling force of 50 N on it. What pulling force (in N) needs to be applied to the cord connecting the larger flywheel of radius 34 cm such that the combination does not rotate? 50 N N

A mass m₁ is attached to a mass m₂ that runs through a hole in a frictionless table as in the figure below. How many rotations per second must the mass m₁ make such that m₂ does not slide down? Assume the radius, r = 0.5 m, and that m₂ is twice the mass of m₁. 4.0 rot/s 2.0 rot/s 1.0 rot/s 3.0 rot/s 5.0 rot/s r m2 m1

Two buckets of mass ?1=17.5 kg and ?2=15.1 kg are attached to the ends of a massless rope which passes over a pulley with a mass of ?p=8.53 kg and a radius of ?p=0.450 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction. The buckets are released from rest and begin to move. If the larger bucket is a distance ?0=2.05 m above the ground when it is released, with what speed ? will it hit the ground?

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.53 m and 1.04 m, respectively. The respective rotational speeds are 456 rev/min and 4,140 rev/min. Calculate the speeds of the tips of both rotors MAIN ROTOR M/S? TAIL ROTOR M/S   Compare these speeds with the speed of sound, 343 m/sv main rotor = ? V SOUND    tail rotor = V SOUND

As shown below, a 32 kg bar that is 4.1 m long is set up to rotate about its center (the yellow circle). Force B is acting 68 cm from the left end of the bar. A = 34 NB = 45 NC = 32 N?A = 56°?B = 24° Find the individual torque, the net torque, and the direction the bar will rotate. ?A = ?B = ?C = ?net =