Rotational Dynamics MCQ Study Notes
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Questions and Answers

What is the maximum speed allowed for a car on a flat circular roadway with twice the radius if it originally had a maximum speed v?

  • 7.5 m/s
  • 4.6 m/s (correct)
  • 2v
  • √2v
  • When a truck carries a load equal to its weight, what is the maximum speed it can take a turn without skidding, if it can take a turn at 12 m/s empty?

  • 12 m/s
  • 24 m/s
  • 6 m/s (correct)
  • 3 m/s
  • What is the tension in the string at the lowest point when a mass m is tied to a string and able to complete a vertical circle?

  • mg
  • 2mg (correct)
  • 4mg
  • 6mg
  • If a particle moves in a circular path with a radius of 0.2 m and an angular speed of 2 rad/s, what will its angular speed be after 0.5 s, given a constant angular acceleration of 4 rad/s²?

    <p>4 rad/s (A)</p> Signup and view all the answers

    What is the tangent of the banking angle related to in terms of speed?

    <p>Inversely proportional to v² (A)</p> Signup and view all the answers

    How many revolutions does a flywheel complete if it slows from 400 rpm to 200 rpm in one minute?

    <p>400 rev (D)</p> Signup and view all the answers

    What is the maximum tension in a string holding a 2 kg mass moving at a speed of 4 m/s in a vertical circle with a radius of 1 m? (g = 10 m/s²)

    <p>72 N (C)</p> Signup and view all the answers

    What is the highest point speed for a small mass m tied to a string that just barely reaches the top of a vertical circle?

    <p>8 m/s (B)</p> Signup and view all the answers

    What is the maximum safe speed of a vehicle on a circular track with a maximum safe speed of 15 km/h when it becomes wet?

    <p>10 km/h (B)</p> Signup and view all the answers

    What is the angular speed of the wheels of a bicycle if their period of rotation is 0.25 seconds?

    <p>8π rad/s (A)</p> Signup and view all the answers

    A car goes around a circular track of radius 50m at a speed of 25 m/s. What is its angular speed?

    <p>5 rad/s (C)</p> Signup and view all the answers

    What is the period of rotation of the wheels of a bicycle if their angular speed is 8π rad/s?

    <p>0.25 s (D)</p> Signup and view all the answers

    What is the ratio of the coefficient of friction of dry track to that of wet track if the maximum speeds are 15 km/h and 10 km/h respectively?

    <p>3:2 (B)</p> Signup and view all the answers

    At what angle should a road be banked for a vehicle to bend a radius of 10 m at a speed of 10 m/s (g = 10 m/s²)?

    <p>45° (B)</p> Signup and view all the answers

    What is the ratio of the speeds of two cars A and B going around concentric tracks of radii R1 and R2 if they take the same time to complete their laps?

    <p>R1:R2 (C)</p> Signup and view all the answers

    What is the direction of the linear velocity in uniform circular motion?

    <p>Tangent to the curve path (D)</p> Signup and view all the answers

    What component provides centripetal acceleration to a car on a circular banked road?

    <p>Horizontal component of normal reaction (A)</p> Signup and view all the answers

    Which of the following physical quantities remain constant for a particle in uniform circular motion?

    <p>Speed and angular velocity (A)</p> Signup and view all the answers

    In uniform circular motion, the position vector, linear velocity, and angular velocity are:

    <p>Mutually perpendicular to each other (A)</p> Signup and view all the answers

    If a body of mass 0.4 kg revolves in a horizontal circle of radius 5m at 120 rev/min, what is the centripetal force acting on it?

    <p>8π² N (A)</p> Signup and view all the answers

    What is the maximum velocity with which a body can be revolved if the breaking tension in the string is 100 N and the radius is 1 meter?

    <p>10 m/s (A)</p> Signup and view all the answers

    When a mass m is tied to a string of length l and whirled in a horizontal circle with a tension F, what will be the tension when the angular velocity is halved?

    <p>F/4 (C)</p> Signup and view all the answers

    What is the angle between the radius vector and centripetal acceleration in circular motion?

    <p>0° (C)</p> Signup and view all the answers

    What happens to the centripetal force if the speed of the body in circular motion is doubled?

    <p>It quadruples (C)</p> Signup and view all the answers

    Flashcards

    Uniform Circular Motion (UCM)

    A motion where an object moves in a circular path at a constant speed.

    Linear Velocity Direction (UCM)

    In uniform circular motion, the direction of linear velocity is tangent to the circular path at any point.

    Constant quantities in UCM

    In uniform circular motion, speed and angular velocity remain constant, while position vector continuously changes.

    Centripetal Force (UCM)

    The force that keeps an object moving in a circular path, directed towards the center of the circle.

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    Relationship between Velocity and Position Vector (UCM)

    In uniform circular motion, velocity is perpendicular to the position vector (radius).

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    Angle between Radius Vector and Centripetal Acceleration

    The angle between the radius vector and centripetal acceleration is 90 degrees.

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    Centripetal Force Calculation

    Centripetal force (F) = mv²/r, where m is mass, v is velocity, and r is the radius of the circular path.

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    Maximum Velocity to avoid Breaking Tension

    When finding maximum velocity in a circular motion, knowing the radius and breaking tension of the string allows calculation.

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    Angular speed of wheels

    The rate of change of angular displacement of a rotating object, measured in radians per second (rad/s).

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    Maximum safe speed (circular track)

    The highest speed a vehicle can maintain on a curved path without skidding, influenced by friction and banking (if applicable).

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    Banking angle

    The angle at which a road is inclined to the horizontal, intended to counteract the centrifugal force acting on a vehicle going around a turn.

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    Centripetal acceleration

    The acceleration experienced by an object in circular motion, directed towards the center of the circle.

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    Ratio of speed (concentric tracks)

    The relationship between the speeds of two vehicles traversing concentric circular tracks in the same time, determined by the radius of each track.

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    Minimum speed at highest point

    The lowest speed required to maintain circular motion in a rotating system, often at the highest point of rotation, preventing free fall or spilling.

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    Coefficient of friction (dry vs wet)

    A measure of the resistance to sliding between two surfaces, affected by the condition of the surface (dry or wet).

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    Angular speed ratio (Clock hands)

    The ratio of the rotational speeds of the hour hand to the earth in a clock or comparable system.

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    Maximum Speed on a Turn

    The highest speed a vehicle can safely navigate a turn without skidding, determined by the friction between tires and road surface and the turn's radius.

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    Effect of Load on Maximum Speed

    When a vehicle's load increases, its maximum safe turning speed decreases due to the increased friction required for the heavier vehicle to turn.

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    Relationship between Banking Angle and Speed

    The angle of a banked curve is directly proportional to the square of the maximum speed a vehicle can safely take the turn.

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    Tension in a String (Vertical Circle)

    The force exerted by a string on an object moving in a vertical circle, varying depending on the object's position.

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    Minimum Speed for Vertical Circular Motion

    The lowest speed an object must have at the top of a vertical circle to maintain its circular path and avoid falling.

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    Angular Acceleration

    The rate of change of angular velocity, representing how quickly an object's rotational speed changes.

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    Flywheel Revolutions

    The number of complete rotations a flywheel makes during a specific time period.

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    Study Notes

    Rotational Dynamics MCQ Study Notes

    • Uniform Circular Motion (UCM): In UCM, physical quantities like speed and angular velocity remain constant, while kinetic energy and radius vector can change. Linear velocity is tangential to the path.

    • Velocity, Position, and Angular Velocity in UCM: These vectors are mutually perpendicular.

    • Angle between Radius Vector and Centripetal Acceleration: The angle is 90°.

    • Ratio of Hour Hand and Earth's Rotation Frequencies: The ratio is 1:12.

    • Angular Speed of Bicycle Wheels: Given angular speed in radians per second, the period of rotation can be calculated (formula needed).

    • Angular Speed of a Car: The angular speed of a car moving on a circular track can be determined given the car's radius and speed. (formula needed).

    • Ratio of Speeds in Concentric Circular Tracks: If two cars, A and B, take the same time to complete laps on concentric tracks with radii R₁ and R₂, respectively, the ratio of car A's speed to car B's speed is R₁/R₂.

    • Centripetal Force Calculation: Given mass, radius, and revolutions per minute, the centripetal force can be calculated. (formula needed)

    • Maximum Velocity in Revolving Object: The maximum velocity with which an object tied to a string can be revolved in a horizontal circle without breaking the string is limited by the string's breaking tension and the object's mass and radius. (formula needed)

    • Tension in String During Circular Motion: The tension in a string supporting a revolving object changes depending on the radius and angular velocity. (formula needed)

    • Horizontal Curve, Maximum Safe Speed Calculation: The maximum safe speed of a car on a banked road depends on the radius of curvature and coefficient of friction. (formula needed)

    • Maximum Safe Speed: The maximum safe speed of a vehicle on a circular track is related to the coefficient of friction between the tires and the road surface. A wetter roadway implies a reduced coefficient of friction.

    • Angle of Banking: The angle of banking of a road is related to the vehicle's speed, radius of curvature, and acceleration due to gravity. Centripetal acceleration is provided by the horizontal component of normal reaction

    • Vertical Circular Motion: Speed needed to avoid spilling water in a bucket rotated vertically. Minimum speed needed to avoid losing contact in a vertical circle.

    • Conical Pendulum: The period of a conical pendulum is related to the length of the string, the radius of the circular path, and the acceleration due to gravity (formula needed).

    • Flywheel Rotational Acceleration: A flywheel's rotational motion, changing its angular speed over time, can be analyzed to determine the number of revolutions in a given time frame or its new angular speed. (formula needed)

    • Vertical Circular Motion Tension: The maximum tension in the string supporting an object in vertical circular motion depends on the object's mass, speed, and radius. (formula needed)

    • Maximum Speed on Banked Curve: The maximum speed a car can safely take a banked turn depends on the angle of banking, the radius of the curve, the coefficient of friction, and acceleration due to gravity. (formula needed)

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    Related Documents

    Rotational Dynamics (MCQ) PDF

    Description

    This quiz focuses on the principles of rotational dynamics, particularly uniform circular motion. It covers concepts like angular speed, centripetal acceleration, and the relationships between different motion variables. Prepare to test your understanding of these critical physics topics.

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