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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?
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?
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?
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?
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?
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?
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?
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?
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What is the tangent of the banking angle related to in terms of speed?
What is the tangent of the banking angle related to in terms of speed?
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How many revolutions does a flywheel complete if it slows from 400 rpm to 200 rpm in one minute?
How many revolutions does a flywheel complete if it slows from 400 rpm to 200 rpm in one minute?
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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)
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)
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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?
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?
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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?
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?
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What is the angular speed of the wheels of a bicycle if their period of rotation is 0.25 seconds?
What is the angular speed of the wheels of a bicycle if their period of rotation is 0.25 seconds?
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A car goes around a circular track of radius 50m at a speed of 25 m/s. What is its angular speed?
A car goes around a circular track of radius 50m at a speed of 25 m/s. What is its angular speed?
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What is the period of rotation of the wheels of a bicycle if their angular speed is 8π rad/s?
What is the period of rotation of the wheels of a bicycle if their angular speed is 8π rad/s?
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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?
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?
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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)?
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)?
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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?
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?
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What is the direction of the linear velocity in uniform circular motion?
What is the direction of the linear velocity in uniform circular motion?
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What component provides centripetal acceleration to a car on a circular banked road?
What component provides centripetal acceleration to a car on a circular banked road?
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Which of the following physical quantities remain constant for a particle in uniform circular motion?
Which of the following physical quantities remain constant for a particle in uniform circular motion?
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In uniform circular motion, the position vector, linear velocity, and angular velocity are:
In uniform circular motion, the position vector, linear velocity, and angular velocity are:
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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?
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?
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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?
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?
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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?
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?
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What is the angle between the radius vector and centripetal acceleration in circular motion?
What is the angle between the radius vector and centripetal acceleration in circular motion?
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What happens to the centripetal force if the speed of the body in circular motion is doubled?
What happens to the centripetal force if the speed of the body in circular motion is doubled?
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Study Notes
Rotational Dynamics MCQ Study Notes
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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.
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Velocity, Position, and Angular Velocity in UCM: These vectors are mutually perpendicular.
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Angle between Radius Vector and Centripetal Acceleration: The angle is 90°.
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Ratio of Hour Hand and Earth's Rotation Frequencies: The ratio is 1:12.
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Angular Speed of Bicycle Wheels: Given angular speed in radians per second, the period of rotation can be calculated (formula needed).
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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).
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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.
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Centripetal Force Calculation: Given mass, radius, and revolutions per minute, the centripetal force can be calculated. (formula needed)
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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)
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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)
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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)
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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.
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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
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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.
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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).
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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)
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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)
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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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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.
