Physics Rotational Mechanics Level: High School
A uniform solid disk with a mass of 28.3 kg and a radius of 0.464 m is free to rotate about a frictionless axle . Forces of 90.0 N and 125 N are applied to the disk , as the picture at “click here” illustrates .(a) What is the net torque produced by the two forces ? ( Assume counterclockwise is the positive direction.)
(b) What is the angular acceleration of the disk ?
Physics Rotational Mechanics Level: High School
Equilibrium
A 1250 N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end . A W = 1940 N crate hangs from the far end of he beam .(a) Calculate the magnitude of the tension in the wire .
(b) Calculate the magnitude of the horizontal and vertical components of the force that the wall exerts on the left end of the beam .
Physics Rotational Mechanics Level: High School
Equilibrium
The drawing shows (at ‘click here’) a person (weight W = 582 N , L1 = 0.827 m , L2 = 0.419 m) doing-push ups . Find the normal force exerted by the floor on each hand and each foot , assuming that the person holds this position .
Physics Rotational Mechanics Level: High School
Equilibrium
The drawings at “click here” shows a lower leg being exercised. It has a F = 59 N weight attached to the foot and is extended at an angle theta with respect to the vertical . consider rotational axis at the knee.(a) When theta is 90 degree , find the magnitude of the torque that the weight creates .
(b) At what angle theta does the magnitude of the torque equal 11 N*m ?
Physics Rotational Mechanics Level: High School
Marble A and marble B , both with the same mass M and radius R , are released at the top of an inclined plane and roll without slipping to the bottom . Marble A is solid , while Marble B is hollow , with all the mass on the surface . If it takes 10.00 seconds for marble A to roll to the bottom , how long does it take for marble B ?
Physics Rotational Mechanics Level: High School
A bicycle wheel has a 30 cm radius . If a smaller wheel with a 25cm radius is installed , what is the change in linear speed if the wheels rotates at 1 rev per second ?
Physics Rotational Mechanics Level: High School
What is the difference between linear speed and rotational speed ? What are the differences in formulas ?
Physics Rotational Mechanics Level: High School
A solid cylindrical disk is to be used as a stabilizer in a ship . By using a massive disk rotating in the hold of the ship , the captain knows that a large torque is required to tilt its angular momentum vector . The mass of the disk to be used is 1.62 x 10^5 kg and it has a radius of 2.05m . If the cylinder rotates at 300.0 rpm , what is the magnitude of he average torque require to tilt it axis by 62.5 degree in a time of 3.03 S? [Hint : Draw a vector diagram of the initial and final angular momenta .]
Physics Rotational Mechanics Level: High School
A figure skater is spinning at a rate of 1.0 rev/s with her arms outstretche . She then draws her arms in to her chest , reducing her rotational inertia to 68% of its original value . What is her new rate of rotation ?
Physics Rotational Mechanics Level: High School
The string in a yo-yo is wound around an axle of radius 0.533 cm . The yo-yo has both rotational and translational motion , like a rolling object , and has mass 0.225 kg and outer radius 1.96 cm . Starting from rest , it rotates and falls a distance of 1.42 m ( the length of the string ). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle .(a) What is the speed of the yo-yo when it reaches the distance of 1.42 m ?
(b) How long does it take to fall ? [Hint: The translation and rotational kinetic energies are related, but the yo-yo is not rolling on its outer radius ]
Physics Rotational Mechanics Level: High School
A solid sphere of mass 0.603 kg rolls without slipping along a horizontal surface with a translation speed of 5.31 m/s . It comes to an incline that makes an angle of 35 degree with the horizontal surface .(a) What is the total energy of the rolling sphere ? Neglect energy losses due to friction .
(b) To what vertical height above the horizontal surface does the sphere rise on the incline ?
Physics Rotational Mechanics Level: High School
A playground merry-go-ground , made in the shape of a solid disk , has a diameter of 2.54 m and a mass of 352.5 kg . Two children , each of mass 30.1 kg , sit on opposite sides at the edge of the platform . Approximately the children as point masses .(a) What torque is required to bring the merry-go-round from rest to 29 rpm in 19.9 S ?
(b) If two other bigger children are going to push on the merry-go-round rim to produce this acceleration, with what force magnitude must each child push ?
Physics Rotational Mechanics Level: High School
A grinding wheel , with a mass of 21.5 kg and a radius of 23.2 cm, is a uniform cylindrical disk .(a) Find the rotational inertia of the wheel about its central axis .
(b) When the grinding wheel’s motor is turned off , friction causes the wheel to slow from 1200 rpm to rest in 59.7 S . What torque must the motor provide to accelerate the wheel from rest to 1200 rpm in 3.98 S ? Assume that the frictional torque is the same regardless of whether the motor is on or off .
Physics Rotational Mechanics Level: High School
A flywheel of mass 185 kg has an effective radius of 0.62 m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel )(a) What torque is required to bring this wheel from rest to a speed of 122 rpm in a time interval of 28.2 s ?
(b) How much work is done during the 28.2 s ?
Physics Rotational Mechanics Level: High School
A bicycle has wheel of radius 0.28 m . Each wheel has a rotational inertia of 0.094 kg.m^2 about its axle . The total mass of the bicycle including the wheels and the rider is 79 kg . When coasting at constant speed , What fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels ?