Exam 9: Solids and Fluids: Part A

A rotating flywheel can be used as a method to store energy.If it has 2.0 × 10⁶ J of kinetic energy when rotating at 435 rad/s,and if a frictional torque of 4.0 N M acts on the system,in what interval of time would the flywheel come to rest?

A bucket of water with total mass 20.0 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder,with crank,at the top of a well.The moment of inertia of the cylinder and crank is 0.21 kg M².The bucket is raised to the top of the well and released to fall back into the well.What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 7.0 m/s?

A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3000 rpm)by an electric motor.The flywheel is a solid cylinder of mass 250 kg and radius 0.500 m (I_cylinder = MR²/2).If the bus requires an average power of 10.0 kW,how long will the flywheel rotate?

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

A box slides down a frictionless incline,and a hoop rolls down another incline.Both inclines have the same height,and both the box and the hoop have the same mass.If both objects start from rest,upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?

A solid disk of radius R rolls down an incline in time T.The center of the disk is removed up to a radius of R/2.The remaining portion of the disk with its center gone is again rolled down the same incline.The time it takes is:

A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest rotational kinetic energy?

A figure skater on ice with arms extended,spins at a rate of 3.5 rev/s.After he draws his arms in,he spins at 6.0 rev/s.By what factor does the skater's kinetic energy change when he draws his arms in?

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s.She then pulls her arms in close to her body.Which of the following results?

A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest angular momentum?

The Earth's density increases with depth.If instead the Earth had uniform density,but the same angular velocity and mass,how would its rotational kinetic energy compare to the actual value?

A hoop,a solid sphere,and a solid cylinder each have the same mass,radius,and initial speed and are going up the same inclined plane.Which one goes the farthest?

An object with mass m and moment of inertia I is spinning with an angular momentum L.Its kinetic energy is:

An astronomical unit (AU)is the average distance from the Earth to the Sun.An comet in orbit around the Sun has a perihelion (near point to the Sun)of 0.50 AU and an aphelion (far point from the Sun)of 5.0 AU.If the comet's orbital speed at aphelion is v,what is its speed at perihelion?

A solid sphere of mass 2.5 kg and radius 0.12 m is at rest at the top of a ramp inclined 15°.It rolls to the bottom without slipping.The upper end of the ramp is 1.2 m higher than the lower end.Find the sphere's total kinetic energy when it reaches the bottom.

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 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 2.5 m/s,what is its total kinetic energy?

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp,inclined 15°,and rolls to the bottom without slipping.(For a cylinder I = 0.5MR². )The upper end of the ramp is 1.5 m higher than the lower end.Find the linear speed of the cylinder when it reaches the bottom of the ramp.(g = 9.8 m/s²)

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 395 rad/s,what maximum energy can be stored?

An astronaut is on a 100-m lifeline outside a spaceship,circling the ship with an angular speed of 0.100 rad/s.How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s²?