Rotational Motion Archives • Page 3 of 4 • Nerd Notes

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What we found:

The figure above shows a uniform beam of length \( L \) and mass \( M \) that hangs horizontally and is attached to a vertical wall. A block of mass \( M \) is suspended from the far end of the beam by a cable. A support cable runs from the wall to the outer edge of the beam. Both cables are of negligible mass. The wall exerts a force \( F_w \) on the left end of the beam. For which of the following actions is the magnitude of the vertical component of \( F_w \) smallest?

Angular momentum cannot be conserved if

When a fan is turned off, its angular speed decreases from \( 10 \) \( \text{rad/s} \) to \( 6.3 \) \( \text{rad/s} \) in \( 5.0 \) \( \text{s} \). What is the magnitude of the average angular acceleration of the fan?

The figure shows a person’s foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?

A wheel of moment of inertia of \( 5.00 \) \( \text{kg} \cdot \text{m}^2 \) starts from rest and accelerates under a constant torque of \( 3.00 \) \( \text{N} \cdot \text{m} \) for \( 8.0 \) \( \text{s} \). What is the wheel’s rotational kinetic energy at the end of \( 8.0 \) \( \text{s} \)?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,

Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

When is the angular momentum of a system constant?

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

Two uniform solid balls, one of radius \( R \) and mass \( M \), the other of radius \( 2R \) and mass \( 8M \), roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?

What condition(s) are necessary for static equilibrium?

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first?

Consider a rigid body that is rotating. Which of the following is an accurate statement?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35° incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by I= (2/5)MR^2.

A planet of constant mass orbits the sun in an elliptical orbit. Neglecting any friction effects, what happens to the planet’s rotational kinetic energy about the sun’s center?

A centrifuge rotor rotating at \( 9200 \) \( \text{rpm} \) is shut off and is eventually brought uniformly to rest by a frictional torque of \( 1.20 \) \( \text{N} \cdot \text{m} \). If the mass of the rotor is \( 3.10 \) \( \text{kg} \) and it can be approximated as a solid cylinder of radius \( 0.0710 \) \( \text{m} \), through how many revolutions will the rotor turn before coming to rest? The moment of inertia of a cylinder is given by \( \frac{1}{2} m r^2 \).

A 0.72-m-diameter solid sphere can be rotated about an axis through its center by a torque of 10.8 N·m which accelerates it uniformly from rest through a total of 160 revolutions in 15.0 s. What is the mass of the sphere?

A rotating merry-go-round makes one complete revolution in 4.0 s. What is the linear speed and acceleration of a child seated 1.2 m from the center?

A centrifuge accelerates uniformly from rest to 15,000 rpm in 240 s. Through how many revolutions did it turn in this time?

A wheel 31 cm in diameter accelerates uniformly from 240rpm to 360rpm in 6.8s. How far will a point on the edge of the wheel have traveled in this time?

A uniform ladder of length L and weight W = 50 N rests against a smooth vertical wall. If the coefficient of static friction between the ladder and the ground is μ = 0.4.

A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam. The beam is uniform, weighs 200 N, and is 6.00 m long. The goodies weigh 80 N.

The system in the Figure is in equilibrium. A concrete block of mass 225 kg hangs from the end of a uniform strut whose mass is 45.0 kg.

An isolated spherical star of radius R, rotates about an axis that passes through its center with an angular velocity of wo. Gravitational forces within the star cause the star’s radius to collapse and decrease to a value ro < Ro, but the mass of the star remains constant. A graph of the star's angular velocity as a function of time as it collapses is shown. Which of the following predictions is correct about the angular momentum L of the star immediately after the collapse?

The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 5.0 rev/s in 8.0 s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 12.0 s. Through how many revolutions does the tub turn during the entire 20-s interval? Assume constant angular acceleration while it is starting and stopping.

A disk of radius \( R = 0.5 \) \( \text{cm} \) rests on a flat, horizontal surface such that frictional forces are considered to be negligible. Three forces of unknown magnitude are exerted on the edge of the disk, as shown in the figure. Which of the following lists the essential measuring devices that, when used together, are needed to determine the change in angular momentum of the disk after a known time of \( 5.0 \) \( \text{s} \)?

A rod may freely rotate about an axis that is perpendicular to the rod and is along the plane of the page. The rod is divided into four sections of equal length of 0.2 m each, and four forces are exerted on the rod, as shown in the figure. Frictional forces are considered negligible. Which of the following describes an additional torque that must be applied in order to keep the rod from rotating?

A 150-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force must be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.500 rev/s in 2.00 s?

A car is moving up the side of a circular roller coaster loop of radius \( 12 \) \( \text{m} \). The angular velocity is \( 1.8 \) \( \text{rad/s} \) and angular acceleration is \( -0.82 \) \( \text{rad/s}^2 \). The car is at the same elevation as the center of the loop. Find the magnitude and direction of the acceleration.

A meterstick with a uniformly distributed mass of 0.5 kg is supported by a pivot placed at the 0.25 mn mark from the left, as shown. At the left end, a small object of mass 1.0 kg is placed at the zero mark, and a second small object of mass 0.5 kg is placed at the 0.5 m mark. The meterstick is supported so that it remains horizontal, and then it is released from rest. One second after it is released, what is the change in the angular momentum of the meterstick?

A rod is initially at rest on a rough horizontal surface. Three forces are exerted on the rod with the magnitudes and directions shown in the figure. The force exerted in the center of the rod is an equidistant 0.5 m from both ends of the rod. If friction between the rod and the table prevents the rod from rotating, what is the magnitude of the torque exerted on the rod about Its center from frictional forces?

An object moves at a constant speed of 9.0 m/s in a circular path of radius of 1.5 m. What is the angular acceleration of the object?

A car accelerates from \( 0 \) to \( 25 \) \( \text{m/s} \) in \( 5 \) \( \text{s} \). If the car’s tires have a diameter of \( 70 \) \( \text{cm} \), how many revolutions does a tire make while accelerating?

During the experiment, students collect data about the angular momentum of a rigid, uniform spinning wheel about an axle as a function of time, which was used to create the graph that is shown. A frictional torque is exerted on the wheel. A student makes the following statement about the data. “The frictional torque exerted on the wheel is independent of the wheel’s angular speed.” Does the data from the graph support the student’s statement? Justify your selection.

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3 rad/s clockwise. The graph shows the point’s angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible.

A student is asked to design an experiment to determine the change in angular momentum of a disk that rotates about its center and the product of the average torque applied to the disk and the time interval in which the torque is exerted. A net force is applied tangentially to the surface of the disk. The rotational inertia of the disk about its center is I = MR”. Which two of the following quantities should the student measure to determine the change in angular momentum of the disk after 10 s? Select two answers.

A platform is initially rotating on smooth ice with negligible friction, as shown at left in the figure. A stationary disk is dropped directly onto the center of the platform. A short time later, the disk and platform rotate together at the same angular velocity, as shown at right in the figure. How does the angular momentum of only the platform change, if at all, after the disk drops? What is a justification for your answer?

A discus is held at the end of an arm that starts at rest. The average angular acceleration of [katex]54 \, \text{rad/s}^2 [/katex] lasts for 0.25 s. Find the average tangential acceleration. Find the speed at release. Find the centripetal acceleration just before release. The path is circular and has radius 1.1 m.

In lacrosse, a typical throw is made by rotating the stick through an angle of roughly 90″, then releasing the ball when the stick is vertical, as shown below. If the stick is at rest when horizontal, the length of the stick is 1 meter, and the ball leaves the stick with a velocity of 10 m/s, what angular acceleration must the stick experience? (31.8 rad / 3)

A horizontal uniform rod of length L and mass M is pivoted at one end and is initially at rest. A small ball of mass M (same masses) is attached to the other end of the rod. The system is released from rest. What is the angular acceleration of the rod just immediately after the system is released?

A horizontal uniform meter stick of mass 0.2 kg is supported at its midpoint by a pivot point. A mass of 0.1 kg is attached to the left end of the meter stick, and another mass of 0.15 kg is attached to the right end of the meter stick. The meter stick is free to rotate in the horizontal plane around the pivot point. What is the tension in the string supporting the left end of the meter stick?

A meter stick of mass 200 grams is balanced at the 40-cm mark when a 100-gram mass is suspended from the 10-cm mark. What is the distance in centimeters from the pivot point to the center of mass of the meter stick?

A meter stick of mass 0.2 kg is pivoted at one end and supported horizontally. A force of 3 N is applied to the free end, perpendicular to the length of the meter stick. What is the net torque about the pivot point?

A 5-meter long ladder is leaning against a wall, with the bottom of the ladder 3 meters from the wall. The ladder is uniform and has a mass of 20 kg. A person of mass 80 kg is standing on the ladder at a distance of 4 meters from the bottom of the ladder. The ladder makes an angle of 60 degrees with the ground. What is the force exerted by the wall on the ladder?