Physics Rotational Mechanics Level: High School
In the figure which is shown at “click here” , the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers . A light rope is wrapped around the cylinder , passes over the pulley , and has a 3.00 kg box suspended from its free end . There is no slipping between the rope and the pulley surface . The uniform cylinder has mass 5.00 kg and radius 40.0 cm . The pulley is a uniform disk with mass 2.00 kg and radius 20.0 cm . The box is released from rest and descends as the rope upwraps from the cylinder . Find the speed of the box when it has fallen 1.50 m .
Physics Rotational Mechanics Level: High School
The pulley in the figure which is shown at “click here” has a radius 0.160 m and a moment of inertia 0.480 kg.m^2 . The rope does not slip on the pulley rim .a) Use energy methods to calculate the speed of the 4.00 kg block just before it strikes the floor .
Physics Rotational Mechanics Level: High School
A stick with a mass ‘m’ and a length of ‘L’ is pivoted about one end so it can rotate without friction about a horizontal axis . The meter stick is held in a horizontal position and released .a) As it swings through the vertical , calculate the change in gravitational potential energy that has occurred . (Use ‘g’ for the acceleration due to gravity )
b) As it swings through the vertical , calculate the angular speed of the stick .
c) As it swings through the vertical , calculate the linear speed of the end of the stick opposite the axis .
d) Find the ratio of the speed of a particle that has fallen a distance of ‘L’ , starting from rest , to the speed from part (C) .
Physics Rotational Mechanics Level: High School
A uniform , solid disk with mass ‘m’ and ‘R’ is pivoted about a horizontal axis through its center . A small object of the same mass ‘m’ is glued to the rim of the disk .a) If the disk is released from rest with the small object at the end of a horizontal radius , find the angular speed when the small objects is directly below the axis .
Physics Rotational Mechanics Level: High School
Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of ‘R’ and a mass of ‘m’ . To prevent structural failure of the flywheel , the maximum allowed radial acceleration of a point on its rim is ‘a’ ?a) What is the maximum kinetic energy that can be stored in the flywheel ?
Physics Rotational Mechanics Level: High School
At a time t , a point on the rim of a wheel with a radius of ‘r’ has a tangential speed of ‘v’ as the wheel slows down with a tangential acceleration of constant magnitude a .a) Calculate the wheel’s constant angular acceleration .
b) Calculate the angular velocity at ‘t’ .
c) Calculate the angular velocity at ‘t = 0’.
d) Through what did the wheel turn between ‘t = 0’ and ‘t’ ?
e) At what time will the radial acceleration equal ‘g’ ?
Physics Rotational Mechanics Level: High School
A high-speed flywheel in a motor is spinning at 440 rpm when a power suddenly occurs . The flywheel has mass 38.0 kg and diameter 80.0 cm . The power is off for 27.0 s and during this time the flywheel slows due to friction in the axle bearings. Determine the time the power is off , the flywheel makes 160 complete revolutions .a) At what rate is flywheel spinning when the power comes back on ?
b) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on ?
c) How many revolutions would the wheel have made during this time ?
Physics Kinematics Level: High School
Flywheel Kinematics
Find the time t 10 it takes to accelerate the flywheel to 10.0 rps (revolutions per seconds) if infinite is 5.00 radians/s^2 .a) Find t 10
b) Find the time t to accelerate that flywheel from rest up to angular velocity w1 .
c) Find the angle B1 through which the flywheel will have turned during the time it takes for it to accelerate from rest up to angular velocity w1 ?
d) Assume that the motor has accelerated the wheel up to an angular velocity w1 with angular acceleration infinite in time t1 . At this point the motor is turned off , and a brake is applied that decelerates the wheel with a constant angular acceleration of -5infinite . Find t2 , the time it will take the wheel to stop after the brake is applied ( that is , the time for the wheel to reach zero angular velocity) .
Physics Rotational Mechanics Level: High School
Kinetic energy of a Rotating Wheel
A simple wheel has the form of a solid cylinder of radius with a mass m uniformly distributed throughout its volume . The wheel is pivoted on a stationary axle through the axis of the cylinder and rotates about the axle at a constant angular speed . The wheel rotates “full revolutions in a time interval”What is the kinetic energy K of the rotating wheel ?
Physics Rotational Mechanics Level: High School
A rope is wrapped around a large wheel that rotates on frictionless bearings through its center and a 2.00 kg mass is attached . The wheel is released and the mass falls a distance of 3.20 meters in a time of 2.50 seconds . The wheel has a radius of .600 meters . What is its moment of inertia ? (The mass hangs from the right side of the wheel ) .
Physics Rotational Mechanics Level: High School
A uniform circular disk has a mass of 12.0 kg and a radius of 30.0 cm . If a constant force of 5.00 N is applied tangential to its edge , what kinetic energy will it have after 30.0 seconds ? Consider the disk a solid cylinder .
Physics Rotational Mechanics Level: High School
Conservation of Angular Momentum
While a merry-go-round rotates at 2.51 rad / s , a child of mass 20.0 kg jumps on the outer edge . The merry-go-round has a mass of 32.0 kg and a radius of 1.00 m . What is the angular speed of the merry go round after child lands ? The child walks halfway toward the center . What is the merry-go-round’s new angular speed ?
Physics Rotational Mechanics Level: High School
Work in Rotational Motion
A solid desk of uniform mass 3.00 kg and diameter 50.0 cm rotates at a rate of 90 rpm . How much work is required to bring it to rest ? If the desk rotates through 4.00 revolutions while coming to rest , how much torque would bring it to rest ?
Physics Rotational Mechanics Level: High School
Rotational Equilibrium
A painter of mass 85.0 kg is on a scaffolding with uniform mass 15.0 kg and length 4.00 m . The scaffolding is suspended by ropes at both ends . If the painter stands 1.20 m from one end , what are the tensions in the two ropes at both end ? Also , if the painter stands at an end of the scaffolding , what are the 2 tensions ?
Physics Rotational Mechanics Level: High School
Equation of Rotational Motion
The blades of a fan run at a low speed at 180.0 rpm . When the fan switches to high speed , the rate of rotation of the blades increases uniformly to 240.0 rpm in 3.14 s . Through how many revolution do the blades go while they are accelerating ?