Physics Rotational Mechanics Level: High School
Centripetal Force
In designing rotating space stations to provide for artificial-gravity environments , one of the constraints that must be considered is motion sickness . Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is fast than approximately 2.2 revolutions per minute . On the other hand , the magnitude of centripetal acceleration at the astronauts feet should equal the magnitude of the acceleration due to gravity on earth . Thus , to eliminate the difficulties with motion sickness , designers must choose the distance between the astronaut’s feet and axis about which the space station rotates to be greater than a certain minimum value , what is this minimum value ?
Physics Rotational Mechanics Level: High School
Centrifugal Force
A block is hung by a string from the inside roof of a van . When the van goes straight ahead at a speed of 30 m / s , the block hangs vertically down . But when the van maintains this same speed around an unbanked curve (radius = 175 m), the block swings toward the outside of the curve . Then the string makes an angle theta with the vertical . Find theta .
Physics Rotational Mechanics Level: High School
Circular Motion
In a skating stunt known as “cracking-the-whip,” a number of skaters hold hands and form a straight line . They try to skate so that the line rotates about the skater at one end , who acts as the pivot . He is skating at a speed of 5.45 m / s . Determine the magnitude of the centripetal force that acts on him .
Physics Rotational Mechanics Level: High School
Rotational Equilibrium
Two identical uniform bricks with lengths (L) of 17 cm are placed in a stack over the edge of a horizontal surface such that the maximum overhang possible without falling is achieved , as in the figure at “click here” . Find the distance x .
Physics Rotational Mechanics Level: High School
Rotational Equilibrium
A 14.5 m uniform ladder weighing 490 N rests against a frictionless wall . The ladder makes a 55.0 degree angle with the horizontal .a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 810 N firefighter forces the ground exerts on the base of the ladder when an 810 N firefighter is 3.70 m from the bottom .
Physics Rotational Mechanics Level: High School
Centre of Gravity
A carpenter’s square has the shape of an L , as shown in the figure at “click here” , where d1 = 21.0 cm , d2 = 2.00 cm , d3 = 2.00 cm , d4 = 10.0 cm . Locate its center of gravity . (Hint : Take(x,y) = (0,0) at the intersection of d1 and d4) .
Physics Rotational Mechanics Level: High School
Conservation of Angular Momentum
A wad of sticky clay of mass m = 5.0 g and velocity v1= 110 m / s fired at a solid cylinder of mass M = 15.0 kg and radius R = 25 cm (see the figure at “click here”) . The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through the center of mass . The line of motion of the projectile is perpendicular to the axle and at a distance d = 22 cm , less than R , from the center .a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder .
b) Is mechanical energy conserved in this process ?
Physics Rotational Mechanics Level: High School
Conservation of Angular Momentum
A student sits on a freely rotating stool holding two weights , each of mass 2.91 kg . When his arms are extended horizontally , the weights are 1.00 m from the axis of rotation and he rotates with an angular speed of 0.759 rad / s . The moment of inertial of the student plus stool is 2.91 kg*m^2 and is assumed to be constant . The student pulls the weights inward horizontally to a position 0.292 m from the rotation axis .a) Find the new angular speed of the student .
b) Find the kinetic energy of the rotating system before and after he pulls the weights inward .
Physics Rotational Mechanics Level: High School
Big Ben (see the figure at “click here”) , the Parliament building tower clock in London, has hour and minute hands with lengths of 2.70 m and 4.60 m and masses of 61.0 kg and 99 kg , respectively . Calculate the total angular momentum of these hands about the center point . Treat the hands as long , thin uniform rods .
Physics Rotational Mechanics Level: High School
A 4.00 kg counterweight is attached to a light cord , which is wound around a spool ( refer the figure at “click here”) . The spot is a uniform solid cylinder of radius 7.00 cm and mass 1.60 kg .a) What is the net torque on the system about the point O ?
b) When the counterweight has a speed v , the pulley has an angular speed of omega = vIR . Determine the total angular momentum of the system about O .
c) Using the fact that r = dL/dt and your result from (b) , calculate the acceleration of the counterweight .
Physics Rotational Mechanics Level: High School
Torque
A particle is located at the vector position r = (i +2j) m , and the force acting on it is F = (5 i + 7 j ) N .a) What is the torque about the origin ?
b) What is the torque about the point having coordinates (0 , 7) ?
Physics Rotational Mechanics Level: High School
A car accelerates uniformly from rest and covers a distance of 56 m in 5.8 s . If the diameter of a tire is 38 cm , find the angular acceleration of the wheel . Answer in units of rad / s^2 .a) Find the final angular velocity of one of the car’s wheels .
b) Find the total number of rotation of the wheel .
Physics Rotational Mechanics Level: High School
A coin is placed 25 cm from the center of a horizontal turntable , initially at rest . The turntable then begins to rotate . When the speed of the coin is 110 cm / s (rotating at a constant rate ) , the coin just begins to slip . The acceleration of gravity is 980 cm / s^2 . What is the coefficient of static friction between the coin and the turntable ?
Physics Rotational Mechanics Level: High School
A racing car travels on a circular track of radius 105 m . The car moves with a constant linear speed of 37.2 m / s . Find the angular speed . Answer in units of rad / s .a) Find the magnitude of its acceleration . Answer in units of m / s^2 .
Physics Rotational Mechanics Level: High School
A flywheel with a very low friction bearing takes 1.1 hours to stop after the motor power is turned off . The flywheel was originally rotating at 41 rpm . What was the initial rotation rate in radians per second ? Answer in units of rad / s .a) How many revolutions does the flywheel make before it stops ? Answer in units of revs .
