A small 700 g ball on the end of a thin, light rod is rotated in a horizontal circle of radius 3.0 m.  Calculate the torque needed to keep the ball rotating at a constant angular speed if the air resistance experienced by the ball is 0.1400 N.   Ignore the rods moment of inertia and air resistance.  Hint:  Treat the small ball as a particle.

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of 50N⋅m50N⋅m. How long does it take the flywheel to reach top angular speed of 1200 rpm?   Show a diagram

A large wind turbine (typical of the size and specifications of a turbine that you see in a modern wind farm) has three blades connected to a central hub. The blades are 50 m long and rotate at 10 rpm. What angular speed ω does this correspond to? What is the speed ν of the tip of a blade? What is the speed of a point 25 m from the hub?

A small 700 g ball on the end of a thin, light rod is rotated in a horizontal circle of radius 2.5 m.  Calculate the torque needed to keep the ball rotating at a constant angular speed if the air resistance experienced by the ball is 0.0200 N.   Ignore the rods moment of inertia and air resistance.  Hint:  Treat the small ball as a particle.

A solid 0.5950 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6550 m. What minimum translational speed ?min must the ball have when it is a height ?=1.008 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s2 for the acceleration due to gravity.

A ball with a weight of 70 N hangs from a string that is coiled around a 3 kg pulley with a radius of 0.4 m. Both the ball and the pulley are initially at rest. The rotational inertia of the pulley is 0.5mr2 and the ball is released from rest. Calculate the ball's velocity after it falls a distance of 2 meters.

An 8.79cm diameter floppy disk rotates at its fastest at 470 rpm.  Part A: Express the angular velocity of the disk in revolutions per seconds?  Part B: What is the time period of this revolution? Use scientific notation for your answer.  Part C: What is the linear velocity of a point at the rim of the disk? Part D: What is the angular velocity at the center of the disk?  Part E: If the disk took 3.2 sec to spin up to 470 rpm from rest, what was the average angular acceleration? How many revolutions did the disk complete within this time? What is the net displacement?  Part F: If you turn off the floppy disk drive and the disk comes to a stop in 6.7 s, what is the average angular acceleration for this period of motion?

A rotating wheel requires 3.0 seconds to rotate through 233.0 radians. Its angular speed at the end of the 3.0-second interval is 98.0 rad/s.  Find: a. The angular speed at the beginning of the 3.0-second interval.  b. The constant angular acceleration of the wheel.

A solid 0.6150 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.7350 m. What minimum translational speed ?minvmin must the ball have when it is a height H=1.111 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?R. Use g=9.810 m/s^2 for the acceleration due to gravity.

A rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per second