Equations of Rotational Motion Practice Problems

The rotational speed of a shaft powered by an electric motor is controlled such that it cannot exceed 450 rev/min. A switching mechanism disconnects power once the shaft hits 450 rev/min. Suppose the shaft has a mass of 36.0 kg and a diameter of 420 mm and power is disconnected at t = 0. The shaft slows down as it delivers power to a load. If it makes 140 revolutions before power is reconnected at t = 23.0 s, what is the rotational speed in RPM at the moment the power is reconnected?

When a motor is switched off, rotational inertia and kinetic energy keep some parts rotating. A shaft experiences a steady decrease in angular frequency changing from 650 rev/min at t = 0 s to 300 rev/min at t = 3.50 s. At what time (t = ? not Δt) does the shaft stop assuming the angular accleration remains the same until it stops?

When an engine is put off, rotational inertia and kinetic energy keep an axle rotating. The axle experiences a steady decrease in angular frequency changing from 420 rev/min at t = 0 s to 160 rev/min at t = 6.40 s. Determine the angular acceleration of the axle in rev/s² and the revolutions it completes from t = 0 s to t = 6.40 s. 

A rotary dining table top lies in the xy plane and rotates about its central axis that is parallel to the z-axis.  At t = 0, the angular velocity of the top, ω_z = -5.00 rad/s. At t = 5.50 s, the angular velocity has increased steadily to +8.50 rad/s. Taking counterclockwise rotation as positive, determine the angular displacement of the disk at t = 5.50 s. 

A disk lies in the xy plane and rotates about its central axis that is parallel to the z-axis.  At t = 0, the angular velocity of the disk, ω_z = -4.80 rad/s. At t = 7.00 s, the angular velocity has increased steadily to +8.90 rad/s. Taking counterclockwise rotation as positive, determine magnitude and state whether the angular acceleration is positive or negative during this time. 

A wind-driven cyclone has a typical diameter of 60.0 cm. Suppose a cyclone has a steady angular acceleration of 0.425 rev/s². At t = 0, it has an angular velocity of 0.500 rev/s. Determine the cyclone's angular velocity and the number of revolutions completed when t = 0.750 s. 

A sprocket is accelerated by a chain from rest at a constant angular acceleration of 5.60 rad/s². If the sprocket has a diameter of 60.0 cm, determine the radial acceleration for a point on the outer edge when the sprocket turns through 5 revolutions using a_rad = ω²r

A toy helicopter is placed in the xy plane with the propeller rotating about its central axis that is parallel to the z-axis.  At t = 0, the angular velocity of the propeller, ω_z = -9.60 rad/s. At t = 12.0 s, the angular velocity has increased steadily to +7.60 rad/s. Taking counterclockwise rotation as positive, determine the time intervals for which the speed is increasing and decreasing. 

The rotor of the centrifuge accelerates a sample tube at a constant rate. The tube is initially at rest. After 35 s of rotation, the tube's angular speed is 1600 rpm. Calculate the tube's angular acceleration.

The disk of a sander machine rotates at a constant speed of 700 rpm. The disk's diameter is 10 cm. Suddenly, the machine fuse blows, and the disk takes 36 s to stop. Calculate the linear velocity of a point on the disk's outer edge 15 s after the fuse blows.

A grinding wheel of radius 8.0 cm rotates clockwise at a constant speed of 650 rpm. Due to a power outage, the wheel completely stops turning in 12s. Calculate the number of revolutions that the wheel makes before stopping.    

A 1.0 kg solid cylinder with a radius of 15 cm is rotating at an angular speed of 230 rpm about its central frictionless axis. You want to stop the cylinder in 30 s by applying a friction force f to the outer edge. Determine the magnitude of f.

The flywheel of a steam engine has a radius of 40 cm. Initially, the flywheel is rotating at 350 rpm about its central axis. The operator enhances the output power from the turbine. As a result, the angular speed rises to 700 rpm in 5 s. Calculate the tangential acceleration of a point located at the outer edge of the flywheel.

What is the angular acceleration of the forearm when it propels a 1.50-kg apple from rest to 8.6 m/s in 0.39 s, solely through elbow rotation driven by the triceps muscle?

What is the angular acceleration experienced by the blades of a cooling system's fan, which operates at 6600 rpm (revolutions per minute) and slows down to rest in 4.3 s when the fan is switched off during operation?

What is the constant angular acceleration of a training centrifuge, which starts from rest and completes 24 full rotations in 1.2 min, used for evaluating trainee astronauts for spaceflight stresses in a training centrifuge?

What is the final angular speed in rpm of a space simulator, which initially starts from rest and completes 24 rotations in 1.2 minutes, aimed at training astronauts for spacecraft maneuvering?

A helicopter landed on a helipad. Soon after, the engine was switched off when the rotor blades were rotating at 730 rev/min. After completing 1120 revolutions, the rotor blades came to a stop. Determine the time the rotor blades took to stop after the engine was shut down.

Three different gear wheels A, B, and C complete a revolution respectively in a minute, an hour, and a day. Express their angular velocities in rad/s and find each of their average angular acceleration.

A planet revolves around a star in 4330 Earth days while it completes a revolution around its own axis in 10.0 hours on Earth. Determine its angular velocity about the star and its own axis.

A wind turbine has a steady angular acceleration of 0.100 rad/s² and an initial angular speed of 0.50 rad/s. Find: i) its angular speed after 4.0 seconds, and ii) the angle the turbine will have turned through between t = 0 and t = 4.0 seconds.