Unvera is operating an apparatus containing a flywheel, which accelerates from rest to its maximum angular speed of 25 rpm, turning through 80 revolutions in the process. How long does Unvera’s flywheel take to accelerate to its maximum speed?

Bilbrun observes his windmill rotate with constant angular speed 6 times in five minutes. Then the wind dies down, and the windmill rotates exactly 3 more times before coming to rest. What is the magnitude of the average angular acceleration of the windmill after it begins slowing down?

Kellen and his crew are training for their next expedition by running laps on a circular track. They complete 2 laps in 580 seconds. If the radius of the track is 191 m, what was their average tangential velocity?

Orryn sets up a mass and pulley system, as shown in the figure. A string is wrapped around a non-uniform pulley of radius 10 cm, which can rotate freely about its center axis. The loose end of the string is attached to a block. The block and pulley each have mass 4.5 kg. If Orryn observes the block accelerate downwards at a rate of 5.5 m/s2, what is the moment of inertia of the pulley?

Bilbrun observes his windmill rotate with constant angular speed 8 times in five minutes. Then the wind dies down, and the windmill rotates exactly 3 more times before coming to rest. What is the magnitude of the average angular acceleration of the windmill after it begins slowing down?

Dalaba swings a small block of mass M = 5.0 kg in a horizontal, circular path on a frictionless surface from a spring. One end of the spring is fixed to the center of the circle and the other end is fastened to the block. The relaxed length of the spring is 25 cm, which then stretches to a total length of R = 30 cm during the circular motion. If Dalaba measures an angular speed of 3.5 rad/s, what is the spring constant for the spring k?

Ellywick decides to try to move through a forest by brachiation, swinging below a handhold to move forward to the next handhold. Weighing 40 kg, Ellywick has an arm length (hand to shoulder) of 0.60 m. We can model her motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of her swing, Ellywick is moving at 3.7 m/s. What upward force must a branch provide to support the swinging Ellywick? 

Fabien leaps off the edge of a cliff, not realizing he would die from the fall. Luckily his friend Gimble snares him with a lasso connected to a 4 m long rope. Once Fabien is hanging stationary with Gimble bravely holding the other end of the rope, Gimble notices that the rope has stretched by 10 cm. Assuming the rope has a diameter of 3 cm and Fabien has a mass of 28 kg, what is the Young’s modulus of the rope?

Orryn sets up a mass and pulley system, as shown in the figure. A string is wrapped around a non-uniform pulley of radius 10 cm, which can rotate freely about its axis. The loose end of the string is attached to a block. The block and pulley each have mass 4.5 kg. If Orryn observes the block accelerate downwards at a rate of 5.2 m/s2, what is the moment of inertia of the pulley?

Unvera is operating an apparatus containing a flywheel, which accelerates from rest to an angular speed of 25 rpm, turning through 55 revolutions in the process. How long does Unvera’s flywheel take to accelerate to its maximum speed?