Chapter 8: Rotational Motion Flashcards
Angular displacement is usually express in units of _______
radians
Angular velocity is usually express in units of _______
radians per second
Angular acceleration is expressed in units of ________
radians per second squared
A boy and a girl are riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?
Both have the same non-zero angular velovity
A boy and a girl are riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the** greater linear speed**?
the boy
A boy and a girl are riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater centripetal acceleration?
the boy
Consider a rigid body that is rotating. Which of the following is an accurate statement?
All points on the body are moving with the same angular velocity
Two equal forces are applied to a door. 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 exerts the greater torque?
the second at the doorknob
What is the quantity used to measure an object’s resistance to changes in rotation?
moment of inertia
Consider two uniform solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is _________
2
Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere’s moment of inertia to that of the smaller sphere is
4
Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on ________
the radius of the sphere
The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth’s angular momentum about the Sun?
It remains constant
The Earth moves about the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?
increases
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?
It does not change
25 revolutions per minute is equivalent to how many rad/s?
2.6 rad/s
A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel’s rotation?
0.50 Hz
A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer rim move in 2.0 s?
41 m
A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wheel?
3.1 rad/s
A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/s without slipping. The maximum centripetal force (provided by static friction) is 1.2 x 10^4 N. What is the mass of the car?
1.5 x 10^3 kg
Suppose that the speedometer of a truck is set to read the linear speed of the truck but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck?
speedometer reads a lower speed than the true linear speed
A grinding wheel 0.35 m in diameter rotates at 2500 rpm.
(a) Calculate its angular velocity in rad/s.
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel?
A centrifuge accelerates uniformly from rest to an angular speed of 15000 rpm (revolutions per minute) in 220 s. Through how many revolutions did it turn in this time?
A person exerts a horizontal force of 32 N on the end of a 96-cm-wide door. What is the magnitude of the torque if the $force is exerted (a) perpendicular to the door and (b) at a
60.0° angle to the face of the door?
A thin uniform rod is free to rotate about an axis directed perpendicular to the screen and passing through its center of mass. Four forces of equal
magnitude are applied to the rod at different locations. Which choice produces the greatest magnitude net torque about the rotation axis?
In case b, the two forces acting at the center produce no torque, while the forces acting at the ends produce torques in the same direction. Each other case features forces acting in opposing directions.
A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.380 kg. Calculate
(a) its moment of inertia about its center
(b) the applied torque needed to accelerate it from rest to 1750 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s
A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much
work is required to accelerate it from rest to a rotation rate of 1.00 revolutions per 8.00 s? Assume it is a solid cylinder.
A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.7 m/s. Calculate its total kinetic energy.
A spherical shell (𝐼 = 2/3 𝑀𝑅^2), a solid sphere (𝐼 = 2/5 𝑀𝑅^2), a thin hoop (𝐼 = 𝑀𝑅^2) and a solid
cylinder (𝐼 = 1/2 M𝑅^2), all with the same mass 𝑀 and radius 𝑅, are released from rest at the top of
an inclined ramp and allowed to roll without slipping. Which object will reach the bottom of the
ramp first?
the solid sphere
A uniform horizontal rod of mass 𝑀 and length ℓ rotates with angular sp
A uniform horizontal rod of mass 𝑀 and length ℓ rotates with angular speed 𝜔 about a vertical axis through its center. Attached to each end of the rod is a small mass 𝑚. Determine the angular momentum of the system about its rotation axis.
If the net force acting on an object is zero, the angular momentum of the object:
may be changing
A playground merry-go-round with a radius of 2.0 m and a rotational inertia of 100 kg * m^2 is rotating at 3.0 rad/s. A child with a mass of 22 kg jumps onto the edge of the merry-go-round, traveling radially inward. What is the new angular speed of the merry-go-round?
A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster such that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms __________
is larger because she’s rotating faster.
A uniform 2.0-kg circular disk of radius 0.2 m is freely rotating about an axis through its center with an angular speed of 𝜔i = 30 rad/s. A second uniform 1.5-kg circular disk of radius 0.15 m that is not rotating is dropped onto the first disk so that the axis of rotation of the first disk passes through the center of the
second disk. What is the final angular speed 𝜔f of the two disks when they are rotating together? Assume static friction acts between the disks after the drop.
A thin, hollow 0.545-kg section of pipe of radius 10.0 cm starts rolling (from rest) without slipping down a 17.5° incline 5.60 m long.
(a) What will be its speed at the base of the incline?
(b) What will be its total kinetic energy at the base of the incline?
