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

Two forces of magnitude 50 N,as shown in the figure below,act on a cylinder of radius 4 m and mass 6.25 kg.The cylinder,which is initially at rest,sits on a frictionless surface.After 1 second,the velocity and angular velocity of the cylinder in m/s and rad/s are respectively

A uniform rod of length (L = 2.0 m)and mass (M = 1.5 kg)is pivoted about a horizontal frictionless pin through one end.The rod is released from rest at an angle of 30° below the horizontal.What is the angular speed of the rod when it passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg⋅m². )

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). -The angular speed of the hour hand of a clock,in rad/s,is

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² starts from rest at t = 0.The wheel has a diameter of 20 cm.What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s².The diameter of the wheel is 40 cm.What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s²?

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s²,in the first 10 minutes?

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes?

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-3.The change in angular position,Δθ,during the 7-second period is

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are negative,its angular velocity is negative,and its angular acceleration is negative.The sphere is

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s² starts from rest at t = 0.At the instant when it has turned through 0.40 radian,what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?

Three particles,each of which has a mass of 80 g,are positioned at the vertices of an equilateral triangle with sides of length 60 cm.The particles are connected by rods of negligible mass.What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?

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 decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?

A uniform rod is 3.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at an angle of 27° above the horizontal.What is the angular speed of the rod as it passes through the horizontal position?

Particles (mass of each = 0.20 kg)are placed at the 40-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 initial angular acceleration of the body?

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper.If M = 2.0 kg and L = 80 cm,what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.

A uniform rod (length = 2.0 m)is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod.If the rod is released from rest in a horizontal position,what is the angular speed of the rod as it rotates through its lowest position?

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.What is her angular displacement (in rad)in the first 8 minutes?

A disk (radius = 8.0 cm)that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s.What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s?

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 cylinder of radius R,mass M,and length L rotates freely about a horizontal axis parallel and tangent to the cylinder,as shown below.The moment of inertia of the cylinder about this axis is