Chapter 5: Uniform Circular Motion and Gravitation - Review Questions

What is the unit of angular velocity?

a) Radians per second

b) Meters per second

c) Degrees per second

d) Revolutions per minute

a) Radians per second

How is the rotation angle Δθ defined?

a) Δθ = Δs/r

b) Δθ = r/Δs

c) Δθ = Δs * r

d) Δθ = r * Δs

a) Δθ = Δs/r

What is the relationship between linear velocity v and angular velocity ω?

a) v = rω

b) v = ω/r

c) v = ωr^2

d) v = ω/r^2

a) v = rω

The rotation angle is defined as the ratio of the arc length to the ___.

radius of curvature

One complete revolution corresponds to an angle of ___ radians.

2π

Explain how angular velocity is related to linear velocity.

Angular velocity is related to linear velocity through the equation v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity. This means that the linear velocity is proportional to both the angular velocity and the radius of the circular path.

Which of the following expressions correctly represents centripetal acceleration in terms of angular velocity?

a) ac = v^2/r

b) ac = rω^2

c) ac = ω^2/r

d) ac = r^2ω

b) ac = rω^2

How does the centripetal acceleration of a centrifuge compare to gravitational acceleration?

a) It is much smaller than gravitational acceleration.

b) It is approximately equal to gravitational acceleration.

c) It is much larger than gravitational acceleration.

d) It is unrelated to gravitational acceleration.

c) It is much larger than gravitational acceleration.

Centripetal acceleration is given by the formula ac = ___, where v is the linear speed and r is the radius of the circle.

v^2/r

In a centrifuge, high centripetal acceleration is used to separate specimens of different ___.

densities

Explain why centripetal acceleration is proportional to the square of the speed in uniform circular motion.

Centripetal acceleration is proportional to the square of the speed because the change in velocity vector, which determines acceleration, depends on both the speed and the direction change. As speed increases, the rate of change of direction increases, leading to a quadratic relationship.

What is the direction of centripetal force in uniform circular motion?

a) Towards the center of curvature

b) Away from the center of curvature

c) Parallel to the velocity

d) Opposite to the velocity

a) Towards the center of curvature

Which of the following expressions represents the centripetal force in terms of mass, velocity, and radius?

a) F_c = m v^2 / r

b) F_c = m r^2 / v

c) F_c = m v / r^2

d) F_c = m r / v^2

a) F_c = m v^2 / r

What happens to the radius of curvature if the centripetal force increases for a given mass and velocity?

a) It decreases

b) It increases

c) It remains the same

d) It becomes zero

a) It decreases

In an ideally banked curve, what is the role of friction?

a) Friction is not needed

b) Friction is essential

c) Friction opposes motion

d) Friction increases speed

a) Friction is not needed

The centripetal force required for uniform circular motion is given by the formula ___ = m v^2 / r.

F_c

Explain why mass cancels out when calculating the static coefficient of friction for a car on a flat curve.

Mass cancels out because friction is proportional to the normal force, which is also proportional to mass. Thus, mass appears in both the numerator and denominator of the equation, allowing it to cancel out.

Which force is responsible for the apparent deflection of moving objects in a rotating frame of reference?

a) Centrifugal force

b) Coriolis force

c) Gravitational force

d) Electromagnetic force

b) Coriolis force

How does the Coriolis force affect weather systems in the northern hemisphere?

a) It causes them to rotate clockwise

b) It causes them to rotate counterclockwise

c) It has no effect

d) It causes them to move in a straight line

b) It causes them to rotate counterclockwise

What is the main difference between centrifugal and centripetal forces?

a) Centrifugal force is real, centripetal is fictitious

b) Centrifugal force is fictitious, centripetal is real

c) Both are real forces

d) Both are fictitious forces

b) Centrifugal force is fictitious, centripetal is real

In a non-inertial frame of reference, fictitious forces such as the ___ force and the ___ force are perceived.

Coriolis; centrifugal

Explain why passengers in a car feel a force pushing them to the side when the car turns.

Passengers feel a force pushing them to the side due to the car's acceleration, which creates a non-inertial frame of reference. This perceived force is a fictitious force because, in reality, the car is changing direction while the passengers tend to continue in a straight line due to inertia.

Describe how the Coriolis force affects the rotation of tropical cyclones in different hemispheres.

The Coriolis force causes tropical cyclones to rotate counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. This is due to the deflection of winds to the right in the northern hemisphere and to the left in the southern hemisphere.

What is the value of the gravitational constant G?

a) 6.674 × 10^11 N⋅m^2/kg^2

b) 6.674 × 10^-11 N⋅m^2/kg^2

c) 9.81 m/s^2

d) 3.00 × 10^8 m/s

b) 6.674 × 10^-11 N⋅m^2/kg^2

What causes the phenomenon of tides on Earth?

a) The gravitational pull of the Sun only.

b) The gravitational pull of the Moon only.

c) The gravitational pull of both the Moon and the Sun.

d) The rotation of the Earth.

c) The gravitational pull of both the Moon and the Sun.

What is the effect of weightlessness experienced by astronauts in orbit?

a) There is no gravitational force acting on them.

b) They are in free-fall, experiencing microgravity.

c) They are outside the influence of Earth's gravity.

d) They experience increased gravitational force.

b) They are in free-fall, experiencing microgravity.

What was the significance of the Cavendish experiment?

a) It measured the speed of light.

b) It determined the value of the gravitational constant G.

c) It proved the existence of black holes.

d) It demonstrated the wave nature of light.

b) It determined the value of the gravitational constant G.

The gravitational force is always ___ and depends only on the ___ involved and the distance between them.

attractive; masses

Explain why the gravitational force is considered the weakest of the four fundamental forces in nature.

The gravitational force is considered the weakest of the four fundamental forces because its strength is significantly less compared to the other forces, such as the electromagnetic force, the strong nuclear force, and the weak nuclear force. This is evident from the small value of the gravitational constant G and the fact that gravitational interactions are only noticeable on a large scale, such as between planets and stars.

Describe the role of the Moon in creating tides on Earth.

The Moon's gravitational pull creates tides on Earth by exerting a force on the Earth's oceans. This force causes a bulge in the ocean on the side of Earth closest to the Moon, creating a high tide. A second high tide occurs on the opposite side of Earth due to the Earth being pulled toward the Moon more than the water on the far side. As Earth rotates, these tidal bulges move, resulting in two high tides each day.

According to Kepler's Second Law, what does an imaginary line from the Sun to a planet do?

a) Sweeps out equal areas in equal times.

b) Remains at a constant distance.

c) Moves faster when closer to the Sun.

d) Moves slower when closer to the Sun.

a) Sweeps out equal areas in equal times.

What is the relationship described by Kepler's Third Law?

a) The square of the period is proportional to the cube of the average distance.

b) The square of the period is proportional to the square of the average distance.

c) The cube of the period is proportional to the square of the average distance.

d) The period is proportional to the average distance.

a) The square of the period is proportional to the cube of the average distance.

Which model of the universe did the Ptolemaic system support?

a) Heliocentric model

b) Geocentric model

c) Elliptical model

d) Parabolic model

b) Geocentric model

What did Newton propose as the cause of Kepler's laws?

a) Electromagnetic force

b) Gravitational force

c) Nuclear force

d) Magnetic force

b) Gravitational force

Kepler's First Law states that the orbit of each planet about the Sun is an ___ with the Sun at one focus.

ellipse