Exam 8: Rotational Equilibrium and Rotational Dynamics

Two children seat themselves on a seesaw.The one on the left has a weight of 400 N while the one on the right weighs 300 N.The fulcrum is at the midpoint of the seesaw.If the child on the left is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the right?

A bucket filled with water has a mass of 23 kg and is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest.Its total kinetic energy at the bottom of the incline:

A 3.0-m rod is pivoted about its left end.A force of 6.0 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque,and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot.The 5.2 N is at an angle of 30 $\degree$ to the rod and causes a cw torque.What is the net torque about the pivot?

A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR².If this cylinder is rolling without slipping along a level surface with a linear speed v,what is the ratio of its rotational kinetic energy to its linear kinetic energy?

If a net torque is applied to an object,that object will experience:

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 550 N in that rope?

A baseball pitcher loosens up his pitching arm.He tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s,what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

A 4.0-kg mass is placed at (3.0,4.0)m,and a 6.0-kg mass is placed at (3.0,-4.0)m.What is the moment of inertia of this system of masses about the y-axis?

Consider the use of the terms "rotation" and "revolution".In physics:

A uniform,horizontal beam of length 6.0 m and weight 120 N is attached at one end to a wall by a pin connection (so that it may rotate).A cable attached to the wall above the pin supports the opposite end.The cable makes an angle of 60 $\degree$ with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

A baseball pitcher,loosening up his arm before a game,tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s,what is the average angular acceleration of the arm and ball?

A 4.0-kg mass is placed at (3.0,4.0)m,and a 6.0-kg mass is placed at (3.0,-4.0)m.What is the moment of inertia of this system of masses about the x-axis?

A uniform 1.0-N meter stick is suspended horizontally by vertical strings attached at each end.A 2.0-N weight is suspended from the 10-cm position on the stick,another 2.0-N weight is suspended from the 50 cm position,and a 3.0-N weight is suspended from the 60 cm position.What is the tension in the string attached at the 100-cm end of the stick?

A bowling ball has a mass of 7.0 kg,a moment of inertia of 2.8 ´ 10^-2 kg*m² and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 4.0 m/s,what is its total kinetic energy?

A meter stick is hinged at its lower end and allowed to fall from a vertical position.If its moment of inertia is ML²/3,with what angular speed does it hit the table?

A bucket of water with total mass 23 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kg*m².If the bucket is raised to the top of the well and released,what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible,that cylinder turns on frictionless bearings and that g = 9.8 m/s². )

A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15 $\degree$ ,and rolls to the bottom.The upper end of the ramp is 1.2 m higher than the lower end.What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4MR² for a solid sphere and g = 9.8 m/s²)

A hoop of radius 1.0 m is placed in the first quadrant of an xy-coordinate system with its rim touching both the x-axis and the y-axis.What are the coordinates of its center of gravity?

A bucket of water with total mass 23 kg is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible,that cylinder turns on frictionless bearings,and that g = 9.8 m/s². )