Exam 9: Rotation

In the figure,the rotational inertia of the wheel and axle about the center is 12.0 kg · m²,the constant force F is 39.2 N,and the radius r is 0.800 m.The wheel starts from rest.When the force has acted through 2.00 m,the rotational velocity $\omega$ acquired by the wheel due to this force will be

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$ /20 s.The angular velocity $\omega$ of the particle is

A homogeneous solid cylinder of mass m,length L,and radius R rotates about an axis through point P,which is parallel to the cylinder axis.If the moment of inertia about the cylinder axis is mR²,the moment of inertia about the axis through P is

In a laboratory experiment,various torques are applied to a rotor and the angular acceleration is measured.The results are plotted on the accompanying graph.From the graph,the moment of inertia of the rotor is

A 5 $\times$ 10^-6-kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 $\times$ 10³ rad/s.The spin axis of the cylinder is vertical and its radius is 0.04 m.The force of adhesion between the paint and the surface is approximately

A uniform stick 1 m long is placed horizontally on the ground along an east-west axis.A force of 1.0 N is applied to the center of the stick in a direction 30º west of north.The torque exerted by the force relative to the east end of the stick is

Two uniform discs,each with the same mass but with radii differing by a factor of two,roll without slipping down an inclined plane.If the two discs start from rest at the same height h,calculate the ratio of the angular velocity of the small disc divided by that of the larger disc.

The disc brake of a high performance car is often made of carbon fiber instead of iron,thereby reducing the mass.If the mass of a carbon disc is that of iron for the same shape and size,by what factor is the moment of inertia changed?

Two objects,m₁ and m₂,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m₁ = m is located at a distance R from the axis of rotation and the second object of mass m₂ = 2m is located at a distance 2R.The angular velocity of mass m₁____ to the angular velocity of m₂.

You give an orbiting satellite a command to rotate through an angle given by where a,b,and c are constants and $\theta$ is in radians if t is in seconds.What is the angular acceleration of this satellite at time t?

Starting from rest,a disk rotates with constant angular acceleration.If it takes 10 rev to reach an angular velocity $\omega$ ,then how many additional revolutions are required to reach an angular velocity 2 $\omega$ ?

A wheel of radius R is rolling without slipping.The velocity of the point on the rim that is in contact with the surface,relative to the surface,is

A wagon wheel consists of 8 spokes of uniform diameter,each of mass m_s and length L cm.The outer ring has a mass m_ring.What is the moment of inertia of the wheel? Assume that each spoke extends from the center to the other ring and the ring is of negligible thickness.

A serious audiophile prefers to listen to music on his vinyl record turntable.The 12-inch diameter disk rotates at a constant 33 rpm.How fast is the record passing by the pickup cartridge tip at a radius of 4 inches? (1 inch = 2.54 cm)

A solid uniform sphere has a density of 3000 kg/m³ when the radius is equal to 0.6 m.If the mass stayed the same but the radius tripled in size,what would the new moment of inertia be for the sphere?

Two small masses,m_A = 4.0 $\times$ 10^-3 kg and m_B = 2.0 $\times$ 10^-3 kg,are connected by a 1.0-m rod of negligible mass.The angular acceleration about B produced by a force of 0.016 N applied at A is approximately

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL²/3.The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is

You have a friend who lives in the southern part of the United States,and you live in the northern part.As Earth rotates,your linear velocity is ___________ hers,and your angular velocity is ____________ hers.

Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a solid cylinder of mass 50 kg and diameter 25 cm.As this cylinder is turned with a crank,the rope raises the bucket.The mass of a bucket of water is 20 kg.Someone cranks the bucket up and then lets go of the crank,and the bucket of water falls down to the bottom of the well.Without friction or air resistance,what is the angular acceleration of the 50-kg cylinder?

A thin,massless string is wrapped around a 0.25m radius grindstone supported by bearings that produce negligible frictional torque.A steady tension of 20 N in the string causes the grindstone to move from rest to a speed of 60 rad/s in 12s.The moment of inertia of the grindstone is