Chapter 5 physics (homework, smart book, and quiz)
According to Kepler's third law, if the average distance from a planet to the Sun increased by a factor of four, then what would happen to the planet's orbital period?
It would increase by a factor of eight.
If both the orbital period and the average distance to the Sun are known for one of the planets, then what can be determined from Kepler's third law?
Mass of the Sun
Rank the following planets in terms of their orbital speed, with the largest orbital speed at the top and the smallest at the bottom.
Planet orbiting a start at a distance of 1x10^11m, and the mass of the star is equal to the mass of the sun Planet orbiting a start at a distance of 1x10^11m, and the mass of the start is equal to half the mass of the sun Planet orbiting a start at a distance of 3x10^11m, and the mass of the start is equal to the mass of the sun Planet orbiting a start at a distance of 3x10^11m, and the mass of the star is equal to half the mass of the sun
What is the direction of the radial acceleration?
Radially inward
The arc length s, subtended by an angle θ in a circle of radius r, is given by s = rθ. In which units must θ be measured?
Radians
A high-speed dental drill is rotating at 3.14 × 104 rad/s. Through how many degrees does the drill rotate in 1.60 s?
Speed Constant = 3.14*10^4 rad/s = w (3.14*10^4 rad/s)(1.60s) = 5.024*10^4 rad Rad to Deg =
The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out. What force keeps the people from falling out the bottom of the cylinder?
Static Friction
Select all of the following effects that are caused by nonzero radial acceleration.
The direction of the object's velocity changes. The object moves around a circle.
Select all of the following statements that are true. The period can be measured in Hertz. The period is equal to the product of 2π and the angular speed. The period is equal to 1 divided by the frequency. The period can be measured in seconds.
The period is equal to 1 divided by the frequency. The period can be measured in seconds.
If we assume the Earth to be perfectly spherical, choose the reasons the apparent weight of an object at rest at the equator is less than the apparent weight of an object at the North Pole.
The radial acceleration is greater.
Select all of the following that are correct. The rate of change of an object's linear velocity is its instantaneous angular acceleration. The rate of change of an object's angular velocity is its instantaneous angular acceleration. α av = ΔωΔt
The rate of change of an object's angular velocity is its instantaneous angular acceleration. α av = Δω/Δt
What is the definition of instantaneous angular acceleration?
The rate of change of the angular velocity
Ice skaters have locked arms and are rotating in a line about a fixed central point. Which skater moves with the largest linear speed?
The skater farthest from the axis of rotation
An object makes three complete rotations in the clockwise direction. What is its angular displacement?
-6π NOTES: The object makes three complete rotations, so the magnitude of the angular displacement is equal to 6π. Clockwise rotations correspond to negative angular displacements.
If the frequency is 50 Hz, then what are the period and angular speed?
0.02 s, 100π rad/s
Four acrobats ride unicycles from one side of the circus tent to the other. The wheels of the unicycles all roll without slipping. Each acrobat travels the same horizontal distance. Rank them according to speed, with the slowest at the top.
10 10 10 30 20 20 10 50
A carnival ride spins its riders in a circle of radius 20 m. The angular speed of the ride is 10 rad/s. What is the magnitude of radial acceleration of the riders?
2000 m/s2
What is the period of a geostationary satellite that orbits the Earth?
24 hours
An object makes one complete rotation. What is the magnitude of its angular displacement?
2π
Select all of the following that are equal to the angle for a complete rotation around a circle.
2π rad 360°
A race car travels once around a circular track of radius 250 meters in 50 seconds at constant speed. What is the magnitude of the car's radial acceleration approximately?
4 m/s2 Rationale: ac = v2/r and v = 2πr/T
Two blocks, one with mass m1 = 0.0500 kg and one with mass m2 = 0.0700 kg, are connected to each other by a string. The inner block is connected to a central pole by another string as shown in the figure with r1 = 0.400 m and r2 = 0.750 m. The blocks are spun around on a horizontal frictionless surface at an angular speed of 1.70 rev/s. What is the tension in the inner string?
4.3 N ((0.0500kg))(0.400m)((1.70 rev/s)(2pi/1))^2 = 2.3 2.3+2 =4.3
Rank the following situations according to the magnitude of the car's tangential acceleration, with the largest magnitude at the top and the smallest at the bottom.
50 1 50 2 20 1 20 2
Rank the following situations according to the magnitude of the car's tangential acceleration, with the largest magnitude at the top and the smallest at the bottom.
500 0.01 100 0.04 200 0.01 100 0.01
An object makes three complete rotations in the counterclockwise direction. What is its angular displacement?
6π
Ice skaters have locked arms and are rotating in a line about a fixed vertical axis of rotation. Which skater moves with the largest angular speed?
All skaters have the same angular speed.
Rank the following sets of data according to the magnitude of the average angular velocity, with the largest magnitude at the top and the smallest at the bottom.
A wheel spins around completely 5 times in 10 seconds A wheel rotates 10 radiant in 5 seconds A wheel rotatse 5 radians in 10 seconds
What is the definition of average angular velocity?
Angular displacement divided by time interval
For a satellite to be geostationary, what must be the shape of its orbit?
Circular
For circular motion to be called uniform circular motion, the speed must remain ________ through out.
Constant
Select all of the following quantities that determine the speed of a planet that is in a stable, circular orbit around a star.
Distance from star to the planet Mass of the star
According to Kepler's first law, what are the shapes of the orbits of all of the planets?
Elliptical
A car travels on a banked circular curve at constant speed. All four of the car's tires roll without slipping. The car moves at just the right speed so that the frictional force is zero. Ignore air resistance. Select all of the following forces that act on the car.
Gravitational Force Normal Force
A conical pendulum is shown in the figure. The mass m moves in a circle of radius r in the horizontal plane. The dashed line is vertical. The string sweeps out the surface of a right circular cone, with the apex of the cone at the top where the string is attached to the ceiling. Which of the following is the radial component of the net force?
Horizontal component of the tension
A tether ball is attached to the top of a vertical pole by a string. The tether ball moves in a circle in the horizontal plane. The string sweeps out the surface of a right circular cone, with the apex of the cone at the top where the string is attached to the top of the pole. Which of the following causes the tether ball to move with uniform circular motion?
Horizontal component of the tension in the string
What is the advantage to banking the plane when making a turn?
It creates a horizontal component to the lift.
How does a centrifuge work?
It uses the object's inertia to move it outward. It creates artificial gravity.
A wheel is spinning around its center at 30 rad/s and a point on its outer edge is moving at 6 m/s. If the angular speed of the wheel is increased, then what will happen to the linear speed of the point on its outer edge?
It will increase.
A car travels on an unbanked circular curve at constant speed. All four of the car's tires roll without slipping. Ignore air resistance. Select all of the following forces that act on the car.
Normal Force Gravitation Force Static Frictional Force
A bicycle wheel has an angular speed of 30 rad/s. Rank the linear speed of a point on the tire with the largest value at the top and the smallest value at the bottom.
Old fashioned adult child
For an object in circular motion, which of the following causes the magnitude of the velocity of the object to change?
Tangential acceleration
Pick the answer that applies to uniform circular motion.
The acceleration is always perpendicular to the motion.
Select all of the following statements that are true regarding ring-shaped space stations that rotate in order to create artificial gravity.
The direction of the apparent gravitational field is radially outward. The floors on the rooms are farthest away from the axis of rotation.
For this question, assume that the Earth is a rotating rigid body. Select all of the following that are true.
The distance between any two points on the surface of the Earth always remains the same. Every point on the surface of the Earth moves in a circular path.
A car travels on an unbanked circular curve at constant speed. All four of the car's tires roll without slipping. Select all of the following statements that are true
The force of friction acts toward the center of the circle. The force of static friction acts on the tires.
Select all of the following statements that are true.
The frequency can be measured in Hertz. The frequency is equal to 1 divided by the period.
An airplane flies in the air around a horizontal circle at constant speed. Which statement is true?
The horizontal component of the lift force acts toward the center of the circle.
A car travels on a banked circular curve at constant speed. All four of the car's tires roll without slipping. The car moves at just the right speed so that the frictional force is zero. Which statement is true?
The horizontal component of the normal force acts toward the center of the circle.
Rank the apparent weight of a person standing on the surface of the Earth at the following locations with the largest apparent weight at the top and the smallest at the bottom. Assume that the Earth is a perfect sphere.
The north geographic... The Arctic Circle The equator
Which of the following would lead to apparent weightlessness?
The only force acting on an object is gravity.
select all of the following equations that are true for apparent weightlessness. W = mg g = 0 a = 0 m = 0 W = 0 a = g
W = mg a = g
Select all of the following that are true for a rigid body.
When a rigid body rotates, every point of the body moves in a circular path. The distance between any two points of the body remains the same when the body translates and/or rotates.
Select all of the following equations that are correct. ar = ω2r ar = v2r ar = v|ω| ar = v2/r
ar = ω2r ar = v|ω| ar = v2/r
A space station is rotating at 30 rad/min, which will create a radial acceleration with a magnitude of g. A delegation of aliens wishes to visit the station. To make them feel welcome, the crew of the station wishes to increase the magnitude of the radial acceleration to approximate the alien's home world's magnitude of acceleration due to gravity. Should they increase or decrease the rotational speed?
increase
What is the amount of time it takes for an object moving in a circle to make one rotation?
period Notes: Angular speed Rationale: Angular speed is the angular distance divided by the time interval. Frequency Rationale: Frequency is how many times an object moves around a circle per unit time.
According to Kepler's third law of planetary motion, the _______ of the period is proportional to the average _______ cubed.
square radius
The four identical wheels of a car all roll without slipping. They all have a radius of 20 cm, and they all spin about their axles at 20 rad/s. How much time does it take the car to travel 100 m along a straight, level road?
v = ωr and v = Δx/Δt 25s
Match each linear variable with its rotational counterpart.
x --> θ v --> w a --> a
Match each kinematic equation for linear motion with constant linear acceleration with its rotational counterpart for rotational motion with constant angular acceleration.
xf = xi + vit + 12 at2 --> θf = θi + ωit + 12 αt2 vf = vi + at--> ωf = ωi + αt vf2 = vi2 + 2a(xf - xi) --> ωf2 = ωi2 + 2α(θf - θi)
Select all of the following that are equal to the magnitude of the average angular velocity of a wheel that spins around once every 2 seconds.
π rad/s 180 degrees/s
Which of the following equations is correct? f = ω ω = 2πf ω = 2πf
ω = 2πf