A gyroscope is a top-like toy consisting of a heavy ring attached by light spokes to a central axle. The axle and ring are free to turn on bearings. To get the gyroscope spinning, a 30-cm-long string is wrapped around the 2.0-mm-diameter axle, then pulled with a constant force of 5.0 N. If the ring’s diameter is 5.0 cm and its mass is 30 g, at what rate is it spinning, in rpm, once the string is completely unwound?

A block (mass = 3.0kg) is hanging from a mass-less string that is wrapped around a pulley. The string is 120cm long. Initially the string was wrapped fully and the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.050m during the block's descent. The mass rolls from rest down to the end of the string. Find the transnational kinetic energy. Find the rotational kinetic energy. Find the angular speed.

A propeller is modeled as five identical uniform rods extending radially from its axis. The length and mass of each rod are 0.867 m0.867 m and 2.51 kg2.51 kg, respectively. When the propellor rotates at 529 rpm529 rpm (revolutions per minute), what is its rotational kinetic energy ??

A bolt requires 272 Nm of torque to be unscrewed. If the maximum force you can apply is 232 N, what is the shortest wrench you can use to unscrew the bolt in cm?

A bike (including wheels) and rider have a combined mass of 68.5 kg and the two wheels of the bike weigh 0.95 kg each. The wheels can be treated as circular hoops. The cyclist freewheels down a hill starting at a speed of 3..25 m/s. What is their speed at the bottom of the hill which is 12m lower than the top?

A 7.2-kg ball is tied to the end of a string.  The ball is then swung at a constant angular velocity of 14 rad/s in a horizontal circle of radius 2.2 m.  What is the torque on the stone?

A 4.00 kg mass is attached to a vertical rod by the means of two 1.25 m strings which are 2.00 m apart. The mass rotates about the vertical shaft producing a tension of 80.0 N in the top string. (a) What is the tension on the lower string? (b) How many revolutions per minute does the system make?

John is pushing his daughter Rachel in a wheelbarrow when it is stopped by a brick 8.00 cm high (see the figure below). The handles make an angle of 0 = 20.0° with the ground. Due to the weight of Rachel and the wheelbarrow, a downward force of 407 N is exerted at the center of the wheel, which has a radius of 18.0 cm. Assume the brick remains fixed and does not slide along the ground. Also assume the force applied by John is directed exactly toward the center of the wheel. (Choose the positive x-axis to be pointing to the right.) & (a) What force (in N) must John apply along the handles to just start the wheel over the brick? 1690.53 X Your response differs from the correct answer by more than 10%. Double check your calculations. N (b) What is the force (magnitude in kN and direction in degrees clockwise from the -x-axis) that the brick exerts on the wheel just as the wheel begins to lift over the brick? magnitude KN direction ° clockwise from the -x-axis

A 24 g block sits at the center of a turntable that rotates at 80 rpm.  A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable.  Calculate the turntable's angular speed when the block reaches the outer edge.  Treat the turntable as a solid disk with mass with mass 200 g and diameter 54.0 cm.  Express your answer in revolutions per minute.

The three 550 g masses in the daigram are connected by massless, rigid rods to form a triangle. What is the triangle's rotational energy (in J) if it rotates at 1.50 rev/s about an axis through the center?