Circular and Harmonic Motion: Master the Basics with Interactive Quizzes

Question 1

A particle moves in a circular path of radius 'r' with constant speed 'v'. Which expression accurately represents the centripetal force acting on this particle?

Accepted Answer

mv^2 / r

Answer

(1/2)mv^2 / r

Answer

2mv^2 / r

Answer

mvr

Question 2

A particle moves in a circle with a constant speed. What is its acceleration?

Accepted Answer

v^2/r

Answer

Zero

Answer

v^2

Answer

rv^2

Question 3

A particle moves in a circular path of radius 'r' with constant speed 'v'. Which of the following statements about the particle's acceleration (a) is correct?

Accepted Answer

It is always perpendicular to the velocity.

Answer

It is zero.

Answer

It is always in the same direction as the velocity.

Answer

It is always in the opposite direction to the velocity.

Question 4

An object moves at a constant speed in a circular path of radius 'r'. In which direction does the object's centripetal acceleration point?

Accepted Answer

Toward the center of the circular path

Answer

In the same direction as the object's velocity

Answer

In the opposite direction to the object's velocity

Answer

Away from the center of the circular path

Question 5

A ball is attached to a 0.5-meter string and spun in a horizontal circle at 2 meters per second. Calculate the centripetal force acting on the ball.

Accepted Answer

4 Newtons

Answer

1 Newton

Answer

8 Newtons

Answer

16 Newtons

Question 6

Which quantity is **not** constant for an object moving in uniform circular motion?

Accepted Answer

Tangential velocity

Answer

Angular velocity

Answer

Centripetal acceleration

Answer

Radius of the circular path

Question 7

A particle of mass m moves in a horizontal circle of radius r with constant angular velocity ω. What is the direction of the centripetal force acting on the particle?

Accepted Answer

Towards the center of the circle

Answer

Away from the center of the circle

Answer

Perpendicular to the velocity of the particle

Question 8

In circular motion, an object moves around a fixed point with a constant angular velocity, ω. Which equation correctly relates the frequency (f) to the angular velocity?

Accepted Answer

f = ω/2π

Answer

f = 2πω

Answer

f = ωπ/2

Answer

f = πω/2

Question 9

An object moves in a circular path at a constant speed. Which of the following statements about the object's velocity and acceleration is true?

Accepted Answer

The object's velocity is always perpendicular to its acceleration.

Answer

The object's acceleration is always zero.

Answer

The object's velocity and acceleration are always in the same direction.

Answer

The object's acceleration is always parallel to its velocity.

Question 10

An object moves at a constant speed in a circular path of radius 'r'. What is the direction and magnitude of its acceleration?

Accepted Answer

Toward the center of the circle, with a magnitude of v^2/r.

Answer

Zero, since the speed is constant.

Answer

In the direction of motion, with a magnitude of v^2/r.

Answer

Away from the center of the circle, with a magnitude of v^2/r.

Question 11

A particle moves in a circle with a constant angular velocity of 2.0 rad/s. If the radius of the circular path is 5.0 m, what is the particle's centripetal acceleration?

Accepted Answer

10.0 m/s²

Answer

2.0 m/s²

Answer

20.0 m/s²

Answer

4.0 m/s²

Question 12

A particle moves in a circle of radius 5 m at a constant speed of 10 m/s. Calculate the period of its motion.

Accepted Answer

6.28 s

Answer

3.14 s

Answer

12.56 s

Answer

25.12 s

Question 13

Which of the following is the SI unit of angular speed?

Accepted Answer

rad/s

Answer

m/s

Answer

m/s^2

Answer

rad/m

Question 14

The equation of a simple harmonic oscillator is given by x = 0.05sin(2πt). What is the amplitude of the motion?

Accepted Answer

0.05 m

Answer

0.025 m

Answer

2π m

Answer

1 m

Question 15

Which of the following applications of simple harmonic motion involves resonance?

Accepted Answer

Radio tuning

Answer

Pendulum clocks

Answer

Seismographs

Answer

Shock absorbers

Question 16

What is the period of a simple pendulum?

Accepted Answer

T = 2π√(L/g)

Answer

T = π√(L/g)

Answer

T = 2π√(g/L)

Answer

T = π√(g/L)

Question 17

What is the amplitude of a simple harmonic oscillator?

Accepted Answer

The maximum displacement from the equilibrium position

Answer

The period of the oscillation

Answer

The acceleration at the equilibrium position

Answer

The energy of the oscillation

Question 18

The energy of a simple harmonic oscillator is given by E = (1/2)kA². What does the constant k represent?

Accepted Answer

Spring constant

Answer

Angular frequency

Answer

Amplitude

Answer

Mass of the oscillator

Question 19

A mass attached to a spring is displaced from its equilibrium position by 'x'. The restoring force exerted by the spring is:

Accepted Answer

-kx

Answer

kx

Answer

-kx^2

Answer

kx^2

Question 20

The angular velocity of a rotating object is expressed in:

Accepted Answer

radians per second

Answer

metres per second

Answer

kilometres per hour

Answer

revolutions per minute

Question 21

In the displacement equation 'x = A cos(ωt)' for a simple harmonic oscillator, 'A' represents:

Accepted Answer

Amplitude

Answer

Frequency

Answer

Phase angle

Answer

Period

Question 22

The amplitude of a simple harmonic oscillator is:

Accepted Answer

The maximum displacement from equilibrium

Answer

The period of oscillation

Answer

The frequency of oscillation

Answer

The acceleration at equilibrium

Question 23

The frequency (f) of a simple harmonic oscillator is:

Accepted Answer

The number of oscillations per second

Answer

The period of oscillation

Answer

The amplitude of oscillation

Answer

The acceleration at equilibrium

Question 24

Which factors affect the period of a simple harmonic oscillator?

Accepted Answer

Both mass and spring constant

Answer

Mass of the object

Answer

Spring constant

Answer

Amplitude of oscillation

Question 25

In a system of coupled oscillators, when one oscillator is driven at its natural frequency, what will happen to the second oscillator?

Accepted Answer

Oscillate at the same frequency as the driving oscillator

Answer

Remain stationary

Answer

Oscillate at twice the frequency of the driving oscillator

Answer

Oscillate at half the frequency of the driving oscillator

Question 26

The formula for centripetal acceleration (a) is:

Accepted Answer

a = v^2 / r

Answer

a = v * r

Answer

a = r^2 / v

Answer

a = v^3 / r^2

Question 27

The force responsible for keeping an object moving in a circular path is called:

Accepted Answer

Centripetal force

Answer

Force of gravity

Answer

Force of friction

Answer

Normal force

Question 28

A particle moves in a circular path of radius 5.0 m. If it completes one revolution in 10.0 s, calculate its angular speed.

Accepted Answer

0.50 rad/s

Answer

0.20 rad/s

Answer

1.00 rad/s

Answer

2.00 rad/s

Question 29

Which graph accurately represents the relationship between displacement and time for an object undergoing simple harmonic motion?

Accepted Answer

A sine curve

Answer

A straight line

Answer

A parabola

Answer

An exponential curve

Question 30

Describe the relationship between the amplitude and energy of an object undergoing simple harmonic motion.

Accepted Answer

Amplitude is directly proportional to energy

Answer

Amplitude is inversely proportional to energy

Answer

Amplitude is not related to energy

Answer

Amplitude is exponentially proportional to energy

Question 31

A 1-meter-long pendulum oscillates with an amplitude of 0.2 m. Determine its maximum angular displacement.

Accepted Answer

0.2 rad

Answer

0.1 rad

Answer

0.8 rad

Answer

0.4 rad

Question 32

What equation represents the centripetal acceleration (ac) of an object moving in a circular path?

Accepted Answer

ac = v^2/r

Answer

ac = v/r

Answer

ac = rv

Answer

ac = r^2/v

Question 33

Which of the following exemplifies an application of circular motion?

Accepted Answer

Centrifuge

Answer

Damped oscillator

Answer

Mass-spring system

Answer

Simple pendulum

Question 34

A particle moves in a circular path of radius 'r' at a constant speed 'v'. Which of the following quantities remains constant throughout the motion?

Accepted Answer

Angular velocity

Answer

Acceleration

Answer

Linear velocity

Answer

Kinetic energy

Question 35

Which of the following is NOT a characteristic of simple harmonic motion?

Accepted Answer

Constant acceleration

Answer

Periodic motion

Answer

Restoring force proportional to displacement

Answer

Energy conservation

Question 36

A particle is moving in a circle. Its centripetal acceleration is:

Accepted Answer

Directed towards the center of the circle

Answer

Directed away from the center of the circle

Answer

Directed perpendicular to the circle

Answer

Zero

Question 37

The period of a simple pendulum is given by:

Accepted Answer

T = 2π√(L/g)

Answer

T = g√(L)

Answer

T = 2π√(g/L)

Answer

T = √(L/g)

Question 38

Which of the following is a real-world application of circular motion?

Accepted Answer

Motion of planets around the Sun

Answer

Free fall of an object

Answer

Motion of a car on a straight road

Answer

Motion of a projectile

Question 39

The amplitude of a simple harmonic oscillator represents:

Accepted Answer

Maximum displacement

Answer

Maximum acceleration

Answer

Maximum energy

Answer

Maximum velocity

Question 40

The restoring force in a simple harmonic oscillator is:

Accepted Answer

Proportional to the displacement

Answer

Proportional to the acceleration

Answer

Proportional to the velocity

Answer

Independent of displacement

Question 41

In circular motion, which of the following is the vector that is always directed towards the center of the circle?

Accepted Answer

Centripetal acceleration

Answer

Tangential acceleration

Answer

Radial acceleration

Answer

Centrifugal force

Question 42

Which of the following is NOT a characteristic of simple harmonic motion?

Accepted Answer

Constant velocity

Answer

Acceleration proportional to displacement

Answer

Periodic motion

Answer

Restoring force proportional to displacement

Question 43

Which of the following is a unit of angular velocity?

Accepted Answer

Radians per second

Answer

Kilometers per hour

Answer

Hertz

Answer

Meters per second

Question 44

Which of the following is a real-world application of circular motion?

Accepted Answer

Clocks

Answer

Tables

Answer

Refrigerators

Answer

Chairs

Question 45

A particle moves in a circle with a constant angular velocity of 2 rad/s. What is the particle's acceleration at any point on the circle?

Accepted Answer

4 m/s²

Answer

2 m/s²

Answer

8 m/s²

Question 46

A particle moves in a circle at constant speed. Which of the following statements about its acceleration is true?

Accepted Answer

It is always directed towards the center of the circle.

Answer

It is always directed away from the center of the circle.

Answer

It is always zero.

Question 47

The displacement of a simple harmonic oscillator is given by x = A cos(ωt + φ). What does φ represent?

Accepted Answer

Phase angle

Answer

Angular frequency

Answer

Time period

Answer

Amplitude

Question 48

Which of the following is a graph of the displacement of a simple harmonic oscillator?

Accepted Answer

A sine or cosine function

Answer

A circle

Answer

A straight line

Answer

A parabola

Question 49

A particle is moving in a circle of radius R. If its angular velocity is ω, what is its linear speed?

Accepted Answer

Rω

Answer

R/ω

Answer

ω/R

Question 50

The period of oscillation for a simple pendulum can be calculated using the formula:

Accepted Answer

T = 2π√(L/g)

Answer

T = 2π√(g/L)

Answer

T = π√(g/L)

Question 51

A particle moves in a circular path with a constant speed. Its acceleration is directed:

Accepted Answer

Towards the center of the circle

Answer

Away from the center of the circle

Answer

Tangent to the circle

Question 52

A mass-spring system is in simple harmonic motion. Increasing which factor will increase the period of oscillation?

Accepted Answer

Mass

Answer

Displacement

Answer

Spring constant

Answer

Amplitude

Question 53

A particle is moving in a circular path with a constant angular acceleration. Which statement about its motion is true?

Accepted Answer

Its tangential acceleration is increasing.

Answer

Its tangential acceleration is decreasing.

Answer

Its radial acceleration is increasing.

Question 54

A simple harmonic oscillator is subject to a damping force. Which of the following effects will damping have on the motion?

Accepted Answer

Decreases the amplitude of oscillation

Answer

Increases the frequency of oscillation

Answer

Increases the period of oscillation

Answer

Has no effect on the motion

Question 55

A particle is moving in a circular path with a radius of 10 cm. If its speed is constant, the relationship between its radial acceleration and its tangential acceleration is:

Accepted Answer

They are equal in magnitude

Answer

They are zero

Answer

Tangential acceleration is greater than radial acceleration

Answer

Radial acceleration is greater than tangential acceleration

Question 56

A ball is attached to a string and swung in a horizontal circle. If the string breaks, what path will the ball follow?

Accepted Answer

The ball will continue in a straight line tangent to the circle at the point where the string broke.

Answer

The ball will fall straight down.

Answer

The ball will continue in a circular path.

Question 57

A mass on a spring oscillates with a period of 4 seconds. What is its frequency?

Accepted Answer

0.25 Hz

Answer

4 Hz

Answer

16 Hz

Question 58

A simple pendulum swings back and forth. At which point in its swing is the pendulum bob's acceleration the greatest?

Accepted Answer

At the endpoints of its swing (where it momentarily stops).

Answer

At the equilibrium position (where it hangs straight down).

Answer

Halfway between the equilibrium position and the endpoints.

Question 59

A mass is attached to a spring and undergoes simple harmonic motion. If the mass is doubled, what happens to the period of oscillation?

Accepted Answer

The period increases by a factor of the square root of 2.

Answer

The period decreases by a factor of 2.

Answer

The period remains the same.

Question 60

A car travels at a constant speed around a circular track. What is the direction of the car's acceleration?

Accepted Answer

Towards the center of the circle.

Answer

There is no acceleration.

Answer

In the direction of the car's velocity.

Answer

Opposite to the direction of the car's velocity.

Question 61

A mass attached to a spring oscillates with a certain amplitude. If the amplitude is doubled, what happens to the maximum speed of the mass?

Accepted Answer

The maximum speed doubles.

Answer

The maximum speed remains the same.

Answer

The maximum speed is halved.

Answer

The maximum speed is quadrupled.

Question 62

A satellite orbits Earth in a circular path. What is the net force acting on the satellite?

Accepted Answer

The force of gravity, specifically Earth's gravitational pull.

Answer

The force of air resistance (negligible in orbit).

Answer

The force of friction (negligible in orbit).

Answer

The force of the satellite's engines.

Question 63

A simple pendulum swings back and forth. What is the restoring force acting on the pendulum bob?

Accepted Answer

The component of gravity acting perpendicular to the pendulum's string (which pulls it back towards the equilibrium position).

Answer

The force of air resistance.

Answer

The force of friction.

Question 64

A mass attached to a spring undergoes simple harmonic motion. What is the energy of the system when the mass is at its maximum displacement?

Accepted Answer

All potential energy.

Answer

All kinetic energy.

Answer

Zero energy.

Answer

Half potential energy and half kinetic energy.