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Quizzes > Science

Constant in Uniform Circular Motion Quiz

20 quick questions with instant feedback. See which quantity remains constant.

Editorial: Review CompletedCreated By: Julie BarnesUpdated Aug 26, 2025
Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art depicting a fun, engaging high school math trivia quiz for self-assessment and test preparation.

This quiz helps you find what stays constant in uniform circular motion and what changes. Answer 20 quick questions to review speed, angular speed, velocity direction, and centripetal acceleration. For more practice, try the forces and motion quiz, check your skills with the speed and acceleration quiz, or refresh basics in a Newton's first law quiz.

In uniform circular motion, which quantity remains constant throughout the motion?
Direction of motion
Speed
Acceleration
Velocity
Uniform circular motion is defined by a constant speed even though the direction of movement continuously changes. While the velocity is a vector that changes direction, the speed remains the same at all points along the circular path.
Which of the following best describes uniform circular motion?
Motion in a straight line at constant speed
Motion in a circle at constant speed
Motion in a circle with increasing speed
Motion along a parabolic path
Uniform circular motion means that an object travels along a circular path with a constant speed. Even though the direction of the object's velocity changes, the speed remains fixed, making the first option the correct description.
In uniform circular motion, the radius of the circular path is:
Oscillating
Decreasing
Increasing
Constant
Uniform circular motion occurs along a circle with an unchanging radius. This fixed distance from the center is one of the defining characteristics of circular motion, making the radius constant throughout.
For an object in uniform circular motion, which of the following remains constant?
Magnitude of velocity
Centripetal acceleration vector
Direction of acceleration
Velocity vector
In uniform circular motion, the magnitude of the velocity, which is the speed, remains constant even though the velocity vector itself is continually changing direction. The other options refer to vector quantities whose directions are always changing.
The term 'uniform' in uniform circular motion refers to:
Constant velocity
Constant acceleration
Constant speed
Consistent change in direction
The word 'uniform' indicates that the object maintains a constant speed throughout its motion along the circular path. Although the object's velocity changes due to a changing direction, its speed remains uniform, which is why constant speed is the correct answer.
For an object in uniform circular motion, which of the following remains constant throughout its motion?
Tangential acceleration
Angular velocity
Resultant acceleration vector
Instantaneous velocity's direction
In uniform circular motion, the angular velocity (ω = v/r) remains constant if both the speed and radius are unchanging. While the direction of the velocity and acceleration vectors continuously varies, the rate at which the object sweeps out angles remains fixed.
For an object moving in a circle with constant speed v and constant radius r, which quantity remains constant?
Instantaneous position
Centripetal force direction
Tangential acceleration
Centripetal acceleration magnitude (v²/r)
When speed and radius are constant, the magnitude of the centripetal acceleration, given by v²/r, remains the same throughout the motion. Although its direction changes as the object moves, its magnitude does not, making it the correct answer.
A particle in uniform circular motion is subject to a centripetal force given by F = m*v²/r. Which aspect of this force remains constant over time?
The magnitude of the centripetal force
The vector sum of centripetal and tangential forces
The work done by the centripetal force per displacement
The direction of the centripetal force
Since the mass, speed, and radius are fixed in uniform circular motion, the magnitude of the centripetal force (m*v²/r) remains constant. Its direction, however, continuously changes as it always points toward the center of the circle.
A car moves with a constant speed of 10 m/s around a circular track with a radius of 5 m. Which of the following remains constant during its motion?
The instantaneous direction of acceleration
The instantaneous velocity vector
Angular velocity
The car's position vector
With a constant speed and fixed radius, the angular velocity (ω = v/r) calculated for the car remains unchanged throughout its motion. Although the car's velocity and acceleration directions change constantly, the angular velocity does not.
In uniform circular motion, which of the following quantities remains unchanged?
Direction of acceleration
Velocity vector
Instantaneous momentum vector
Magnitude of velocity
The key characteristic of uniform circular motion is that the speed, or the magnitude of the velocity, remains constant. Even though the velocity vector changes direction, its magnitude does not vary, making it the correct answer.
How does the centripetal acceleration behave in uniform circular motion when the speed remains constant?
Its magnitude varies while its direction remains fixed
Its magnitude is constant while its direction continually changes
It is zero at all times
Both its magnitude and direction are constant
In uniform circular motion the centripetal acceleration is always directed toward the center of the circle; its magnitude (v²/r) remains constant when speed and radius are constant. However, the direction of this acceleration changes continuously as the object moves.
In uniform circular motion, what is the correct relationship between linear speed (v) and angular speed (ω)?
ω = r/v
ω = v/r
v = ω/r
v = ωr²
The linear speed and angular speed in circular motion are related by the formula ω = v/r. This means that if both v and r are constant, then ω remains constant as well. The other options do not correctly express this relationship.
An object in uniform circular motion follows the period equation T = 2πr/v. If both the radius and speed remain constant, which quantity is unchanging?
The period T
The instantaneous linear displacement
The arc length between successive positions
The changing direction of the velocity vector
Given that the radius and linear speed are constant, the period T (the time required for one complete revolution) calculated by T = 2πr/v will also be constant. Other quantities, such as instantaneous displacement or velocity direction, change continuously.
What is the work done by the centripetal force on an object in uniform circular motion?
Dependent on the object's mass
Zero
Dependent on the angular displacement
Equal to the kinetic energy of the object
The centripetal force always acts perpendicular to the displacement of an object in uniform circular motion. Because work is the component of force in the direction of displacement, the work done by a perpendicular force is zero.
Which geometric property of the circular path remains constant in uniform circular motion?
The chord length between successive positions
The radius of the circle
The variable distance from different points to the center
The length of the arc over a fixed time interval
The constant radius is a defining characteristic of uniform circular motion. While other measurements along the path, such as chord lengths or arc segments over time, may vary depending on the position, the radius remains unchanged.
A particle in uniform circular motion has a constant speed v around a circle of radius r. If the speed were doubled, which of the following would change compared to its original motion?
The mass of the particle
The uniformity of the motion
The magnitude of the centripetal acceleration
The radius of the circular path
Doubling the speed while keeping the radius constant increases the centripetal acceleration by a factor of four, since a = v²/r. The particle's mass and the radius remain unchanged, and the motion can still be uniform even though the acceleration magnitude is different.
Consider two objects in uniform circular motion on concentric circles. Object A has speed v and radius r, while Object B has speed 2v and radius 2r. Which of the following quantities is identical for both objects?
Centripetal force
Centripetal acceleration
Linear momentum
Angular speed
Angular speed is given by ω = v/r. For Object A it is v/r, and for Object B it is (2v)/(2r), which simplifies to v/r as well. Although their linear speeds and centripetal accelerations differ, their angular speeds are identical.
A particle in uniform circular motion experiences a net inward force. If one incorrectly assumes that the particle's velocity remains unchanged in both magnitude and direction, what misconception might arise?
That the mass of the particle decreases over time
That the radius of the circular path is variable
That there is no acceleration acting on the particle
That the centripetal force increases the particle's speed
Assuming the velocity does not change in direction implies that there is no acceleration, since acceleration is the rate of change of velocity. In reality, even though the speed is constant, the continuous change in the direction of the velocity vector produces a centripetal acceleration.
During uniform circular motion, which statement about angular displacement is accurate?
Angular displacement oscillates between positive and negative values
Angular displacement remains fixed over each cycle
Angular displacement increases linearly with time
Angular displacement is constant because the object returns to the starting point
With a constant angular speed, the angular displacement increases linearly over time, following the relation θ = ωt. Even though the object may return to its starting position after a complete cycle, the total angular displacement keeps accumulating.
For an object undergoing uniform circular motion, if T represents the period of revolution, which of the following quantities remains constant regardless of the object's position along the circular path?
The period T
The instantaneous displacement from the circle's center
The instantaneous momentum vector
The instantaneous velocity vector
The period T, defined as the time required for one complete revolution, is a fixed value in uniform circular motion when speed and radius are constant. In contrast, the instantaneous displacement, velocity, and momentum vectors continually change as the object moves along the circle.
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Study Outcomes

  1. Understand the concept of uniform circular motion and its associated constant values.
  2. Identify the constant parameters in scenarios involving uniform circular motion.
  3. Apply formulas to calculate and validate constant values such as angular velocity.
  4. Analyze the relationship between angular speed and radius in a circular path.
  5. Evaluate self-assessment problems to reinforce the comprehension of constants in circular motion.

Uniform Circular Motion Constant Cheat Sheet

  1. Speed remains constant - In uniform circular motion, the object travels equal arcs in equal time slices, so the speed never wavers as it zooms around the circle. Picture a race car keeping a steady pace even as it hugs every bend.
  2. Tangential velocity direction changes - While the magnitude of tangential velocity stays the same, its head spins around constantly as the object orbits the center. Imagine the needle of a spinning compass always pointing sideways to keep you on track.
  3. Centripetal acceleration points inward - This acceleration always aims at the circle's center and has magnitude ac=v²/r, linking how fast you go to how tight the curve is. It's like the invisible hand steering a satellite around Earth.
  4. Centripetal force keeps you turning - The net force pulling you inward equals Fc=m·ac=m·v²/r, balancing mass, speed, and curve radius. Whether it's tension in a string or friction on a tire, that force is your roundabout guide.
  5. Angular velocity is uniform - Denoted ω, this spin rate stays constant and links directly to linear speed via v=r·ω, tying together distance from center and how quickly you rotate. Think of RPM on your bike wheel!
  6. Period stays the same - The time T for one full loop never changes, and ω=2π/T ties rotation rate to how long each lap takes. It's like the beat of a metronome for circular motion.
  7. Frequency is constant - Revolutions per second f=1/T remain steady, measured in hertz (Hz). Think of it as the circular motion's "song," humming at a fixed pitch.
  8. Radius stays fixed - You keep the same distance from the center, so r never wiggles during the motion. Changing r would crank up or chill out your acceleration - so it's crucial to stay locked in.
  9. Net force magnitude is constant - All forces combine to give a steady inward pull equal to Fc, so you never get a surprise push or pull. It's the physics equivalent of cruise control in radial forces.
  10. Centripetal acceleration is always radial - Perpendicular to the path's tangent, this acceleration vector always points toward the center, making sure the object bends its path without speeding up or slowing down. Imagine an invisible leash keeping you on the circular track.
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