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WorksheetsSTEM GENPHYS1 THIRD QTR EXAM
Total questions: 12
Worksheet time: 43mins
The principle of the moment of inertia, or rotational inertia, is that an object's resistance to changes in its rotational motion is determined by its mass and how that mass is distributed relative to an axis of rotation. It is analogous to mass in linear motion, meaning a larger moment of inertia requires more torque to change the object's angular velocity. For a collection of point masses, the moment of inertia is the sum of each mass multiplied by the square of its distance from the axis of rotation.
Based on the principle of moment of inertia, which statement correctly describes how an object’s rotational inertia is affected by its mass distribution?
The moment of inertia decreases when mass is placed closer to the axis of rotation.
The moment of inertia increases when mass is placed farther from the axis of rotation.
The moment of inertia remains constant regardless of mass distribution.
The moment of inertia decreases when torque is applied to the axis of rotation.
Which of the following statements correctly describe the principle of moment of inertia?
(SELECT ALL THAT APPLY)
It depends on both the mass of an object and how that mass is distributed relative to the axis of rotation.
It represents an object’s resistance to changes in its rotational motion or angular velocity.
It is analogous to mass in linear motion, requiring more torque to change angular velocity when larger.
It depends only on the torque applied and not on the distribution of mass.
A solid disk of mass 2 kg and radius 0.5 m rotates about its central axis. What is its moment of inertia?
(ANSWER WITH UNIT ONLY)
(a)
Torque is a vector quantity that measures the tendency of a force to cause rotational motion about an axis. It is defined as the cross product of the position vector and the force vector.
Which statement best describes the principle of torque based on its definition as a cross product?
Torque is the product of mass and acceleration acting on an object.
Torque is the product of force and distance measured along the direction of the force.
Torque is the vector product of the position vector and the force, determining rotational effect.
Torque is the scalar product of the position vector and the force, determining linear motion.
Which of the following statements correctly describe the principle of torque as a cross product?
(SELECT ALL THAT APPLY)
Torque is a vector quantity that causes rotational motion about an axis.
The magnitude of torque depends on the force, the lever arm, and the sine of the angle between them.
The direction of torque is determined using the right-hand rule.
Torque is calculated by multiplying the force and distance in the same direction.
A force of 20 N is applied at the end of a 0.5 m wrench at an angle of 90° to the handle. What is the magnitude of the torque produced about the pivot point? (ANSWER WITH UNIT ONLY)
(a)
Rotational quantities such as angular displacement, angular velocity, and angular acceleration are expressed as vectors because they have both magnitude and direction. Their direction is determined by the right-hand rule, pointing along the axis of rotation. This vector representation helps describe how objects rotate and relate rotational motion to torque and angular momentum.
Which statement best describes why rotational quantities are represented as vectors?
Because they only have magnitude and no direction.
Because they describe both the size and direction of rotational motion.
Because they depend only on the mass of the rotating object.
Because they are always perpendicular to the axis of rotation.
Which of the following statements correctly describe rotational quantities using vectors?
(SELECT ALL THAT APPLY)
Rotational quantities have both magnitude and direction along the axis of rotation.
The direction of rotational vectors is determined using the right-hand rule.
Angular velocity and angular acceleration are examples of rotational vector quantities.
Rotational quantities are always measured in linear units of distance and time.
How are angular velocity, angular acceleration, and torque related when described as vectors?
They all act along the axis of rotation and follow the right-hand rule for direction.
They all act perpendicular to the axis of rotation and follow the left-hand rule for direction.
They all act along the plane of rotation and have no specific direction.
They all act opposite to the axis of rotation and depend only on linear speed.
A system is in static equilibrium when it remains at rest and all forces and torques acting on it are balanced. This means the net force on the system is zero, preventing linear motion, and the net torque is zero, preventing rotational motion.
Which condition must be satisfied for a system to be in static equilibrium?
The net force acting on the system must be zero.
The system must be moving at a constant velocity.
The net torque acting on the system must be increasing.
The system must have unbalanced forces acting on it.
Which of the following conditions must be met for a system to be in static equilibrium?
(SELECT ALL THAT APPLY)
The net force acting on the system must be equal to zero.
The net torque acting on the system must be equal to zero
The system must remain at rest without any acceleration.
The system must have a constant nonzero velocity.
How are the conditions of net force and net torque related in determining static equilibrium?
Both must be zero to ensure the system remains at rest without rotation.
Both must be maximum to keep the system balanced and stationary.
Both must be equal in magnitude but opposite in direction to maintain rest.
Both must act in the same direction to prevent any motion or rotation.
When a system rotates with constant angular acceleration, its motion can be described using rotational kinematic equations that relate angular displacement, angular velocity, angular acceleration, and time. These equations are analogous to linear kinematics but apply to rotational motion around an axis.
Which of the following statements correctly describe rotational kinematic relations for constant angular acceleration? (SELECT ALL THAT APPLY)
Angular velocity changes uniformly over time when angular acceleration is constant.
Angular displacement depends on initial angular velocity, angular acceleration, and time.
The equations of rotational motion are similar in form to linear kinematic equations.
Angular acceleration varies with time when torque is constant.
How are angular displacement, angular velocity, and angular acceleration related in rotational motion with constant angular acceleration?
Angular displacement depends on both angular velocity and angular acceleration over time.
Angular displacement depends only on the initial angular velocity and not on acceleration.
Angular velocity depends only on angular displacement and not on acceleration.
Angular acceleration depends only on angular displacement and not on time.
The angular momentum of a system measures the quantity of rotational motion it possesses and depends on the moment of inertia and angular velocity. For a rigid body, it is the product of its moment of inertia and angular velocity, while for a particle, it is the cross product of its position vector and linear momentum. Angular momentum is conserved when no external torque acts on the system.
Which of the following statements correctly describe the angular momentum of different systems?
(SELECT ALL THAT APPLY)
The angular momentum of a rigid body equals the product of its moment of inertia and angular velocity.
The angular momentum of a particle equals the cross product of its position vector and linear momentum.
The total angular momentum of a system is conserved when no external torque acts on it.
The angular momentum of a system depends only on its mass and not on its velocity.
How are moment of inertia, angular velocity, and angular momentum related in a rotating system?
Angular momentum increases when either moment of inertia or angular velocity increases.
Angular momentum decreases when both moment of inertia and angular velocity increase.
Angular momentum remains constant regardless of changes in angular velocity.
Angular momentum depends only on the mass of the rotating object and not on its rotation.
A system is in static equilibrium when the net force and net torque acting on it are both zero, meaning the system remains at rest without rotation or translation. In contexts such as see-saws, cable-hinge-strut systems, leaning ladders, and weighing objects with scales, solving static equilibrium involves applying the conditions ∑F = 0 and ∑τ = 0 to determine unknown forces, torques, or positions that maintain balance.
How are forces and torques related in maintaining static equilibrium in a system?
Both the net force and net torque must be zero to keep the system in complete equilibrium.
The net force must be zero, but the net torque can have any nonzero value for balance.
The net torque must be zero, but the net force can have any nonzero value for rest.
Both the net force and net torque must be nonzero to maintain the system’s stability.
A uniform 2-meter long see-saw is balanced at its center. A child weighing 300 N sits 0.5 m from one end. At what distance from the other end should another child weighing 200 N sit to keep the see-saw in equilibrium? (formula: W1d1 = W2d2) (ANSWER WITH UNIT)
(a)
Newton’s Law of Universal Gravitation states that every mass attracts every other mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This gravitational force determines an object’s weight near a planet’s surface and defines the acceleration due to gravity (g) as the gravitational force per unit mass.
How are gravitational force, weight, and acceleration due to gravity related according to Newton’s Law of Gravitation?
Weight is the gravitational force acting on a mass, and acceleration due to gravity is the force per unit mass.
Weight is independent of gravitational force, and acceleration due to gravity depends only on mass.
Gravitational force and weight are unrelated, but both depend on the square of the distance.
Acceleration due to gravity increases with distance, while gravitational force remains constant.
Find the gravitational force between the Earth and a 2 kg object located on its surface.
(Take the mass of Earth, M = 5.97 × 10²⁴ kg, radius of Earth, r = 6.37 × 10⁶ m, and gravitational constant, G = 6.67 × 10⁻¹¹ N·m²/kg².) [ANSWER WITH UNIT ONLY)
(a)
The gravitational field represents the region around a mass where another mass experiences a gravitational force. Its strength at any point is defined as the force per unit mass acting on a small test mass placed at that point. It describes how massive bodies influence the motion of other objects without direct contact, illustrating the continuous and universal nature of gravitational interaction.
Which of the following statements correctly describe the physical significance of a gravitational field?
(SELECT ALL THAT APPLY)
It is the region around a mass where another mass experiences a gravitational force.
It represents the force per unit mass acting on a small test mass at a point.
It shows how masses interact through direct physical contact.
It explains how massive bodies influence other objects without touching them.
How does the gravitational field relate to the gravitational force experienced by a mass?
The gravitational field determines the force per unit mass acting on an object at a point in space.
The gravitational field increases only when the object’s mass becomes smaller in value.
The gravitational field exists only when two objects are in direct physical contact.
The gravitational field remains constant regardless of the distance between two masses.
Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the object’s mass, the acceleration due to gravity, and its height above a reference point. In physics problems, this concept is used to analyze energy transformations, determine work done by gravity, and solve for motion or equilibrium in systems influenced by gravitational forces.
Which quantity directly affects the gravitational potential energy of an object?
The mass of the object and its height above the ground
The color of the object and its surface texture
The temperature of the object and its density
The shape of the object and its volume
Which of the following statements correctly describe gravitational potential energy?
(SELECT ALL THAT APPLY)
It depends on the mass of the object and its height above a reference level.
It increases when an object is lifted higher in a gravitational field.
It is the energy an object has due to its motion in a straight line.
It can be calculated using the expression ( U = mgh ).
Planetary and satellite motion is governed by the balance between gravitational force and the centripetal force required for circular or elliptical orbits. By applying Newton’s Law of Gravitation and the laws of motion, quantities such as orbital velocity, period, and acceleration can be calculated. These relationships explain how celestial bodies maintain stable orbits under the influence of gravity.
How are gravitational force and orbital velocity related in maintaining a satellite’s circular orbit around a planet?
The gravitational force provides the centripetal force that keeps the satellite moving in its circular path.
The gravitational force acts opposite to the centripetal force, slowing the satellite’s orbital motion.
The gravitational force increases the satellite’s mass to maintain its circular orbital speed.
The gravitational force and orbital velocity are independent and do not affect each other’s magnitude.
A satellite is orbiting the Earth at a height where the radius of its orbit is 7.0 × 10⁶ m. Calculate its orbital velocity.
(Take the mass of Earth, M = 5.97 × 10²⁴ kg, and gravitational constant, G = 6.67 × 10⁻¹¹ N·m²/kg².)
(a)
Kepler’s Third Law states that the square of a planet’s orbital period is proportional to the cube of its orbital radius. This relationship can be derived from Newton’s Law of Gravitation and the concept of centripetal acceleration by equating the gravitational force to the centripetal force required for circular motion. This shows that orbital motion is governed by the gravitational attraction between the planet and the Sun, linking orbital period, radius, and mass through fundamental physical laws.
Which statements correctly explain how Kepler’s Third Law connects with Newton’s Law of Gravitation and centripetal acceleration in circular orbits?
(SELECT ALL THAT APPLY)
The gravitational force provides the centripetal force that maintains a planet’s circular orbit.
The orbital period squared is directly proportional to the cube of the orbital radius.
The gravitational constant and the mass of the central body determine the orbital period.
The centripetal acceleration is independent of the gravitational attraction between bodies.
How does Newton’s Law of Gravitation explain Kepler’s Third Law for planets in circular orbits?
By showing that the gravitational force acts as the centripetal force, linking orbital period and radius.
By proving that gravitational force and orbital period are completely independent of each other.
By stating that the gravitational force increases as the orbital period decreases linearly.
By suggesting that the centripetal acceleration is unrelated to the gravitational attraction.
