Exam 10: Rotation of a Rigid Object About a Fixed Axis

A wheel (radius = 12 cm)is mounted on a frictionless,horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel.A light cord wrapped around the wheel supports a 0.40-kg object.If released from rest with the string taut,the object is observed to fall with a downward acceleration of 3.0 m/s².What is the moment of inertia (of the wheel)about the given axle?

A uniform rod (length = 2.4 m)of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end.The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass.The rod is released from rest when it is horizontal.What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point?

Two cylinders made of the same material roll down a plane inclined at an angle θ with the horizontal.Each travels the same distance.The radius of cylinder B is twice the radius of cylinder A.In what order do they reach the bottom?

A solid sphere,a solid cylinder,and a hoop all have the same mass and radius.Each are sent down identical inclined planes starting from rest.Their kinetic energies at the bottom of the incline are K_sphere, K_cylinder,and K_hoop.Which of the following is true?

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J.What is the moment of inertia of the propeller?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?

A rigid rod of length l rotates about an axis perpendicular to the rod,with one end of the rod fixed to the axis.Which of the following are equal at all points on the rod? I. The angular position II. The angular velocity III. The angular acceleration IV. The centripetal acceleration V. The tangential acceleration

A mass m = 4.0 kg is connected,as shown,by a light cord to a mass M = 6.0 kg,which slides on a smooth horizontal surface.The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg⋅m².The cord does not slip on the pulley.What is the magnitude of the acceleration of m?

Particles (mass of each = 0.40 kg)are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass.This rigid body is free to rotate about a frictionless pivot at the 0-cm end.The body is released from rest in the horizontal position.What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?

Four identical particles (mass of each = 0.24 kg)are placed at the vertices of a rectangle (2.0 m × 3.0 m)and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle?

A wheel (radius = 0.20 m)starts from rest and rotates with a constant angular acceleration of 2.0 rad/s².At the instant when the angular velocity is equal to 1.2 rad/s,what is the magnitude of the total linear acceleration of a point on the rim of the wheel?

Which of the following diagrams shows the greatest magnitude net torque with a zero net force? All the rods,of length 2r,rotate about an axis that is perpendicular to the rod and fixed in the center of the rod.All the forces are of magnitude F or 2F and all distances from the axis are r or r/2.

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

Four identical particles (mass of each = 0.40 kg)are placed at the vertices of a rectangle (2.5 m × 4.0 m)and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?

A uniform rod (mass = 2.0 kg,length = 0.60 m)is free to rotate about a frictionless pivot at one end.The rod is released from rest in the horizontal position.What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal?

When the center of a bicycle wheel has linear velocity Relative to the ground,the velocity relative to the ground of point P' at the top of the wheel is

A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm.Assuming the Frisbee,a uniform disk,is originally at rest and the force is exerted for 0.08 s,determine the angular velocity of rotation about the central axis when the Frisbee is released.

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis is

A solid sphere,a solid cylinder,a spherical shell,and a hoop all have the same mass and radius.Each are rolling on a horizontal surface with the same center of mass speed,and then they roll up identical inclines.Which one goes the greatest distance up its incline?