Exam 8: Rotational Equilibrium and Dynamics

The torque caused by a force F applied at a distance r from the axis of rotation,is given by τ = rF​sinθ,where θ is the angle between And )If the magnitudes r and F remain the same,what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?

A hoop,solid sphere,and solid cylinder each have the same mass and same radius.When rolling down the same incline,which has the greatest torque from gravity on it?

A turntable has a moment of inertia of 3.00 × 10−² kg·m² and spins freely on a frictionless bearing at 25.0 rev/min.A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?

An initially installed flywheel can store 10⁶ J of kinetic energy when rotating at 300 rad/s.It is replaced by another flywheel of the same size but made of a stronger material.If its mass is the same as that of the original,and it is now capable of achieving a rotational speed of 425 rad/s,what maximum energy can be stored?

​Anika and Sam are astronauts floating in space outside their spaceship.They are tethered together by a rope of length 10.5 m.They both begin pulling on the rope at the same time.Anika has mass of 80 kg,and Sam 100 kg.Because her mass is less,Anika reaches the middle of the rope first.Assuming the center of the rope is at the origin and that Anika and Sam start at 5.25 m and -5.25 m,respectively,where is Sam when Anika reaches the middle?

A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by KE = Mv² when rolling down an incline.What is this object's moment of inertia?

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.70 m long and each ball on the end is 0.10 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

A 3.00-kg mass is placed at (2.00,3.00)m,and a 4.50-kg mass is placed at (2.00,−3.00)m.What is the moment of inertia of this system of masses about the y axis?

A hoop (I = MR²)is rolling along the ground at 10 m/s.It comes to a hill and starts going up.Assuming no losses to friction,how far does it travel vertically up the hill before it stops?

A bank vault is opened by applying a force of 140 N perpendicular to the plane of the door,1.20 m from the hinges.Find the torque due to this force about an axis through the hinges.

A ventilation fan with a moment of inertia of 0.0340 kg·m² has a net torque of 0.110 N M applied to it.If it starts from rest,what kinetic energy will it have 10.4 s later?

A solid sphere and a solid cylinder both have the same radius and mass.If the sphere is spun about an axis through it center with angular velocity _sphere,what angular velocity must the cylinder have to the same rotational kinetic energy as the sphere? Round your answer to 2 significant figures.

A "double satellite" is launched into space.It consists of a satellite of mass m and another satellite of mass 5m.The connecting mechanism of these satellites is an explosive bolt and a compressed spring,both of negligible mass.The bolt is exploded and the satellites drift apart having been pushed by the spring.When the less massive satellite has moved a distance of 2.5 m from the center of mass of the double satellite,how far away from it is the satellite of greater mass?

A turntable has a moment of inertia of 3.0 × 10−² kg·m² and spins freely on a frictionless bearing at 25 rev/min.A 0.60-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.10 m from the center.By what factor does the kinetic energy of the system change after the putty is dropped onto the turntable?

A bucket of water with total mass 26 kg is attached to a rope,which in turn is wound around a 0.04-m radius cylinder at the top of a well.A crank with a turning radius of 0.20 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.11 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. )

Two children seat themselves on a seesaw.The one on the left has a weight of 300 N while the one on the right weighs 200 N.The fulcrum is at the midpoint of the seesaw.If the child on the right 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 left? (Take ccw as positive. )

The quantity "angular momentum" (in terms of the fundamental quantities of mass,length,and time)is equivalent to:

A baseball pitcher loosens up his pitching arm.He tosses a 0.140-kg ball using only the rotation of his forearm,0.270 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.425 s,what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

An object of mass m and moment of inertia I has rotational kinetic energy KE_R.Its angular momentum is:

A 274-N uniform ladder,11.0 m long,rests against a smooth vertical wall.The coefficient of static friction between ladder and floor is 0.400.What minimum angle can the ladder make with the floor before it slips?