Physics Unit 2: Two-Dimensional Motion

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Questions and Answers

What term describes the path followed by a projectile?

Line of motion

Velocity vector

Acceleration path

Trajectory (correct)

Which of the following statements is true regarding the horizontal motion of a projectile?

Horizontal velocity remains constant neglecting air resistance. (correct)

Horizontal motion is dependent on vertical motion.

Horizontal motion is accelerated due to gravity.

Horizontal velocity changes uniformly.

What is the value of the constant downward acceleration experienced by a projectile due to gravity?

10.00 m/s²

9.80 m/s

5.00 m/s²

9.80 m/s² (correct)

In projectile motion, how are the horizontal and vertical components of motion related?

They are analyzed independently. Signup and view all the answers

Which scenario describes a horizontal projectile?

A water hose spraying water horizontally. Signup and view all the answers

Why can projectile motion equations not be applied directly to vertical motion in inclined cases?

Inclined angles change the initial vertical velocity. Signup and view all the answers

What happens to the horizontal component of velocity when air resistance is negligible?

It remains constant throughout the motion. Signup and view all the answers

The analysis of which components of projectile motion fail to consider the effects of gravity?

Horizontal components only. Signup and view all the answers

What does torque measure in the context of rotational motion?

The effectiveness of a force in causing rotation Signup and view all the answers

Which variable is connected to torque and moment of inertia in rotational dynamics?

Angular acceleration Signup and view all the answers

Kepler's First Law states that planets move in what type of orbits?

Elliptical orbits Signup and view all the answers

What factor does NOT affect the moment of inertia of an object?

Speed of rotation Signup and view all the answers

In the equation τ = Iα, what does the symbol I represent?

Moment of inertia Signup and view all the answers

Which of the following best describes the lever arm in terms of torque?

The distance from the axis of rotation to the point where force is applied Signup and view all the answers

According to Kepler's laws, what happens to a planet's distance from the Sun during its orbit?

It varies throughout the orbit Signup and view all the answers

How is torque calculated if a force is applied at an angle?

By considering the component of force perpendicular to the lever arm Signup and view all the answers

What unit is used to measure angular displacement?

Radians Signup and view all the answers

How is angular velocity defined?

The rate of change of angular displacement Signup and view all the answers

Which equation correctly relates linear speed to angular speed?

v = rω Signup and view all the answers

What does angular acceleration measure?

The change in angular velocity Signup and view all the answers

Why is the right-hand rule used in rotational motion?

To visualize the direction of angular quantities Signup and view all the answers

In what way are the equations for rotational motion similar to those for linear motion?

They have analogous equations for constant acceleration Signup and view all the answers

What is one full revolution in radians?

$2 ext{π} ext{ rad}$ Signup and view all the answers

Which of the following is NOT a quantity associated with rotational motion?

Linear Displacement Signup and view all the answers

Study Notes

Unit 2: Two-Dimensional Motion

Two-dimensional motion describes objects moving in paths that are not straight lines.
Projectile motion is a type of two-dimensional motion where an object moves through the air, affected only by gravity.
- Examples include a football, basketball, or water droplets from a fountain.
- The trajectory of a projectile is curved.
- The motion can be analyzed by separating it into horizontal and vertical components.
Horizontal motion is independent of vertical motion.
- Horizontal velocity remains constant (neglecting air resistance).
Vertical motion is affected by gravity.
- Vertical acceleration is constant (9.80 m/s² downward).
- Vertical velocity changes.
There are essential equations for describing projectile motion that provide information about position, velocity, and time of flight.
Horizontal and inclined projectiles are covered separately in the unit.
- Horizontal projectiles have zero initial vertical velocity.
- Inclined projectiles have both horizontal and vertical components to their initial velocity.

Rotational Motion

Rotational motion involves objects moving in circular paths around a fixed axis.
Key quantities include:
- Angular displacement (θ): Measured in radians.
- Angular velocity (ω): Rate of change of angular displacement (rad/s).
- Angular acceleration (α): Rate of change of angular velocity (rad/s²).
The right-hand rule is used to determine the direction of angular velocity and acceleration vectors.
Linear and angular quantities are related.
- Example: Linear speed (v) = radius (r) × angular speed (ω).

Rotational Dynamics

Dynamics of rotational motion concern the factors causing rotations.
Torque (τ): The turning force, depending on force magnitude, the lever arm (distance from the axis), and the angle of force application.
- τ = rFsin(θ)
Moment of inertia (I): Describes an object's resistance to changes in rotational motion.
- Depends on the mass of an object and the distribution of mass relative to the axis of rotation.
Torque, moment of inertia, and angular acceleration are related.
- τ = Iα

Kepler's Laws and Newton's Law of Universal Gravitation

Kepler's First Law: Planets move in elliptical orbits around the sun, with the sun at one focus.
Kepler's Second Law: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
- Planets speed up when closer to the sun and slow down when farther away.
Kepler's Third Law: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. (T² ∝ r³)
Newton's Law of Universal Gravitation: Every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- F = G(m₁m₂)/r²
- G is the gravitational constant.
Newton's Law provides a theoretical foundation for Kepler's empirically derived laws.

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Description

Explore the concepts of two-dimensional motion, focusing on projectile motion and the effects of gravity. This quiz will test your understanding of horizontal and vertical components, as well as the equations that describe the trajectories of various projectiles. Prepare to analyze how objects move through different paths in two dimensions.