Physics Honors - Uniform Circular Motion

To accelerate an object moving in a straight line, the applied force must be ________________ to the direction of motion.

parallel

To increase the velocity of an object moving in a straight line, apply a force in the ________ direction of the object's motion.

same

To decrease the velocity of an object moving in a straight line, apply a force in the ________________ direction of the object's motion.

opposite

Centripetal Force

A force that keeps an object moving in a circular path.

Centripetal Acceleration

The acceleration produced by centripetal force.

To move an object along a circular path, a net force must be applied towards the ____________ of the circular path.

center

Is it possible for an object moving with a constant speed to accelerate? Explain.
A. No, if the speed is constant, the acceleration equals zero.
B. No, an object can accelerate only if a net force is acting on it.
C. Yes, although the speed is constant, the direction of the velocity can change.
D. Yes, if an object is moving, it can experience acceleration.

C

An object moves in a circular path at a constant speed. Compare the direction of the object's velocity and acceleration vectors.
A. Both vectors point in the same direction.
B. The vectors point in opposite directions.
C. The vectors are perpendicular.
D. The question is meaningless, since the acceleration is zero.

C

What type of acceleration does an object moving with constant speed in a circular path experience?
A. Free Fall
B. Constant Acceleration
C. Linear Acceleration
D. Centripetal Acceleration

D

Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity.
A. It is moving in a straight line.
B. It is moving in a circle.
C. It is moving in a parabola.
D. None of the above is definitely true all of the time.

B

What force is needed to make an object move in a circle?
A. Kinetic Friction
B. Static Friction
C. Centripetal Force
D. Weight

C

When an object experiences uniform circular motion, the direction of the net force is...
A. in the same direction as the motion of the object.
B. in the opposite direction of the motion of the object.
C. is directed toward the center of the circular path.
D. is directed away from the center of the circular path.

C

Period

The time it takes an object to complete one trip around a circular path. The symbol for this is "T." This is measured in seconds.

What equation(s) can be used to find the period?

ᵗ⁄ₙ (time over number of trips)
¹⁄f (1 over frequency)
T = ²πʳ⁄ᵥ

What is the period of the second hand on a clock?
A. 60 seconds
B. 1 hour
C. 12 hours
D. It depends on the time.

A

What is the period of the minute hand on a clock?
A. 60 seconds
B. 1 hour
C. 12 hours
D. it depends on the time.

B

What is the period of the hour hand on a clock?
A. 60 seconds
B. 1 hour
C. 12 hours
D. it depends on the time.

C

If it takes 50 seconds for an object to travel around a circle 5 times, what is the period of its motion?
A. 0.1 seconds
B. 1 second
C. 5 seconds
D. 10 seconds

D

If a runner can make a full trip around a small track in 90 seconds, how much time would it take to complete 6 loops of the track?
A. 6 seconds
B. 15 seconds
C. 540 seconds
D. 900 seconds

C

If an object is traveling in circular motion and its period is 3 seconds, how many revolutions will it complete in one minute?
A. 15
B. 20
C. 30
D. 60

B

Frequency

The number of revolutions that an object completes in a given amount of time. The symbol for this is f and is measured in Hertz (Hz).

What equation(s) can be used to find frequency?

ⁿ⁄ₜ (number of revolutions over time)
¹⁄T (1 over period)

An object travels around a circle 50 times in ten seconds, what is the frequency of its motion?
A. 0.2 Hz
B. 2.5 Hz
C. 5 Hz
D. 10Hz

C

If a wheel spins with a frequency of 8 Hz, how much time will it take to spin around 16 times?
A. 0.5 seconds
B. 1 second
C. 2 seconds
D. 4 seconds

C

If an object is traveling in circular motion with a frequency of 7 Hz. How many revolutions will it make in 20 seconds?
A. 2.8 Revolutions
B. 3 Revolutions
C. 14 Revolutions
D. 140 Revolutions

D

The greater the period, the ______________ the frequency.

smaller

The smaller the period, the ______________ the frequency.

greater

Period is the inverse of ________________.

frequency

Frequency is the inverse of ____________.

period

An object has a period of 4 seconds. What is the frequency of its motion?
A. 0.25 seconds
B. 2 seconds
C. 4 seconds
D. 5 seconds

A

An object is revolving with a frequency of 8 Hz. What is its period?
A. 0.1 seconds
B. 0.13 seconds
C. 4 seconds
D. 8 seconds

B

What equation(s) can be used to find angular velocity?

²πʳ⁄T (2πr over period)

2πrf

sqrt(rg)

sqrt(GM⁄ᵣ)

An object is in circular motion. The radius of its motion is 2 meters and its period is 5 seconds. What is its velocity?
A. 1.3 m/s
B. 2.5 m/s
C. 5 m/s
D. 10 m/s

B

An object is in circular motion. The radius of its motion is 2 meters and its velocity is 20 m/s. What is its period.
A. 0.31 seconds
B. 0.62 seconds
C. 1.3 seconds
D. 2.5 seconds

B

An object is in circular motion. The period of its motion is 2 seconds and its velocity is 20 m/s. What is the radius of its motion?
A. 2.1 meters
B. 6.4 meters
C. 13 meters
D. 20 meters

B

An object is in circular motion. The radius of its motion is 3 meters and its frequency is 0.25 Hz. What is its velocity?
A. 0.75 m/s
B. 2.4 m/s
C. 4.7 m/s
D. 12 m/s

C

An object is in circular motion. The radius of its motion is 2 meters and its velocity is 30 m/s. What is its frequency?
A. 1.2 Hz
B. 2.3 Hz
C. 16 Hz
D. 60 Hz

B

An object is in circular motion. The frequency of its motion is 7 Hz, and its velocity is 20 m/s. What is the radius of its motion?
A. 0.45 meters
B. 0.9 meters
C. 1.8 meters
D. 7 meters

A

What equation(s) can be used to find angular acceleration?

ᵛ²⁄ᵣ (velocity squared over radius)

An object is traveling with a velocity of 6 m/s in a circular path whose radius is 4 meters. What is the magnitude of its centripetal acceleration?
A. 3 meters
B. 6 meters
C. 9 meters
D. 18 meters

C

An object is traveling with a velocity of 6 m/s in a circular path. Its acceleration is 3 m/s². What is the radius of its path?
A. 20 meters
B. 4 meters
C. 8 meters
D. 12 meters

D

An object is traveling in a circular path whose radius is 65 meters. Its acceleration is 3 m/s². What is its velocity?
A. 4 m/s
B. 7 m/s
C. 14 m/s
D. 18 m/s

C

An object is traveling in a circle with a radius of 2 meters at a period of 4 seconds. Find its acceleration.
A. 2.4 m/s²
B. 4.9 m/s²
C. 8.8 m/s²
D. 11 m/s²

B

An object is traveling in a circle with a radius of 2 meters at a frequency of 3 Hz. Find its acceleration.
A. 79 m/s²
B. 350 m/s²
C. 480 m/s²
D. 710 m/s²

D

An object is traveling in a circular path whose radius is 65 meters. Its acceleration is 3 m/s². What is the period of its motion.
A. 48 seconds
B. 29 seconds
C. 68 seconds
D. 86 seconds

B

What equation(s) can be used to find the net force in uniform circular motion?

ᵐᵛ²⁄ᵣ (mass times velocity squared over radius)

A car with a mass of 1800 kg goes around an 18 meters radius turn at a speed of 35 m/s. What is the centripetal force on the car?
A. 25,000 N
B. 75,000 N
C. 120,000 N
D. 250,000 N

C

A ball on a string spins in a horizontal circle of radius 2.5 meters with a speed of 3 m/s. The tension in the string is 5.4 N. What is the mass of the ball?
A. 1.5 kg
B. 3 kg
C. 3.6 kg
D. 4.8 kg

A

A 75 kg mass is attached to the end of a 5-meter-long metal rod string, which rotates in a horizontal circular path. If the maximum force that the rod can withstand is 8500 N, what is the maximum speed that the mass can attain without breaking the rod?
A. 15 m/s
B. 24 m/s
C. 25 m/s
D. 110 m/s

B

What is the net force on a 2 kg mass spinning in a circle with a radius of 1.5 meters and a frequency of 4 Hz?
A. 3 N
B. 19 N
C. 380 N
D. 1900 N

D

_____________ force, force of ________________, force of ______________, and force of ______________ can all act as a centripetal force.

Normal
friction
gravity
tension

True/False: Centrifugal force does not exist.

True

A boy stands at the edge of a rotating table. Which of the following forces prevents him from sliding off the table?
A. Force of Gravity
B. Normal Force
C. Static Friction
D. Kinetic Friction
E. None from the above.

C

A boy stands at the edge of a rotating table. In order to keep him moving in a circular path, the table applies a certain force on the boy. Which of the following is the reaction force to this force?
A. The normal force on the boy.
B. The force of gravity exerted on the boy by Earth.
C. The force of gravity exerted on Earth by the boy.
D. The force exerted on the table by the boy that is directed straight down.
E. The static friction force exerted by the boy on the table.

D

A 55 kg man is driving a car at a constant speed of 10 m/s. What is his apparent weight when he is traveling on a section of the road that is completely flat?

550 N

A 55 kg man is driving a car at a constant speed of 10 m/s. What is his apparent weight as he drives over the very top of a hill that has a radius of 25 meters?

330 N

A 55 kg man is driving a car at a constant speed of 10 m/s. What is his apparent weight as he drives down the very bottom of a drip that has a radius of 25 meters?

770 N

What equation(s) can be used to find gravity?

ᵛ²⁄ᵣ (velocity squared over radius)
GM⁄ᵣ²

When a car is traveling over the top of a hill, the driver and passengers will have ______________________________________________ compared to driving at the same speed on a flat road.
A. a lower apparent weight
B. the same apparent weight
C. a higher apparent weight
D. a lower or higher apparent weight depending on the height of the hill

A

When a car is traveling through a dip in the road, the driver and passengers will have ________________________________________________ compared to driving at the same speed on a flat road.
A. a lower apparent weight
B. the same apparent weight
C. a higher apparent weight
D. a lower or higher apparent weight depending on the height of the hill

C

When a car is traveling over the top of a hill, the driver and passengers will feel weightless when their velocity equals ________________.
A. gr
B. -gr
C. sqrt(gr)
D. ᵍ⁄ᵣ

C

A car is traveling at a velocity of 20 m/s over the top of a hill of radius 80 meters. The driver's mass is 60 kg. What is the apparent weight of the driver at the top of the hill?
A. 0 N
B. 290 N
C. 590 N
D. 890 N

B

At what velocity must a car drive over a hill of radius 80 meters if the driver and car are to appear weightless?
A. 12 m/s
B. 28 m/s
C. 46 m/s
D. 58 m/s

B

A pilot executes a vertical dive, then follows a semi-circular arc until going straight up. At their lowest point, the normal force acting on the pilot is...
A. less than mg and pointing up.
B. less than mg and pointing down.
C. more than mg and pointing up.
D. more than mg and pointing down.

C

Gravity acts as a ______________________ force to keep the moon in orbit around the Earth.

centripetal

The sideways (tangential) ________________ vector makes sure that it doesn't crash into Earth.

velocity

Newton's 3d law states that the gravitation force by Earth on the moon to keep it in orbit is __________ and ________________ to the force exerted on Earth by the moon.

equal
opposite

Force is ________________ proportional to mass 1 and mass 2.

directly

Force is __________________ proportional to the distance between mass 1 and mass 2.

inversely

What is the value of G?

6.67 ⋅ 10⁻¹¹ Nᵐ²⁄ₖg²

The value of __ is what converts the large numbers you get from substituting values of mass.

G

Gravity is an extremely _________ force, which is why we don't all stick together. The only time gravity because noticeable is when one of the masses is ________.

weak
huge

What is the magnitude of the gravitational force acting on a 4 kg object, which is 1 meter from a 1 kg object?
A. 3.3 ⋅ 10⁻¹¹ N
B. 1.7 ⋅ 10⁻¹¹ N
C. 2.7 ⋅ 10⁻¹⁰ N
D. 6.7 ⋅ 10⁻¹¹ N

C

What is the magnitude of the gravitational force between Earth and its moon?
r = 3.8 ⋅ 10⁸ meters
mₑₐᵣₜₕ = 6 ⋅ 10²⁴ kg
mₘₒₒₙ = 7.3 ⋅ 10²² kg
A. 2 ⋅ 10¹⁸ N
B. 2 ⋅ 10¹⁹ N
C. 2 ⋅ 10²⁰ N
D. 2 ⋅ 10²¹ N

C

________________ that has mass has a gravitational field.

Anything

The ____________ the mass, the larger the gravitational field.

larger

What would happen to the gravitational field if you started burrowing into the ground?

It would start to shrink.

A car moves around a circular path of a constant radius at a constant speed. Which of the following statements is true?
A. The car's velocity is constant.
B. The car's acceleration is constant.
C. The car's acceleration is zero.
D. The car's velocity is directed toward the center.
E. The car's acceleration is directed toward the center.

E

A car moves around a circular path of a constant radius at a constant speed. When the car is at the top of the circular path, what is the direction of the velocity?
A. ⮕
B. ⬇
C. ⬅
D. ⬆
E. ⬊

C

A car moves around a circular path of a constant radius at a constant speed. When the car is at the top of the circular path, what is the direction of the acceleration?
A. ⮕
B. ⬇
C. ⬅
D. ⬆
E. ⬊

B

An object moves in a circular path at a constant speed. Which of the following is true?
A. The car's acceleration is zero because it has a constant speed.
B. The car's acceleration is not zero and causes the car to slow down.
C. The car's acceleration is not zero and causes the car to speed up.
D. The car's acceleration is not zero and causes the change in the direction of the car's velocity.
E. None from the above.

D

A small sphere is swung in a vertical circle. Which of the following combinations represents the direction of the velocity and acceleration at the bottom of the circle?
A. v ⬆ | a ⮕
B. a ⬆ | v ⮕
C. v ⬆ | a ⬇
D. v ⬆ | a ⬅
E. v ⬅ | a ⬇

B

A small sphere is swung in a vertical circle. Which of the following combinations represents the direction of the velocity and acceleration at the right-most point of the circle?
A. v ⬆ | a ⮕
B. a ⬆ | v ⮕
C. v ⬆ | a ⬇
D. v ⬆ | a ⬅
E. v ⬅ | a ⬇

D

An object experiences a uniform circular motion in a horizontal plane and the left-most point of the circle. What is the direction of the net force?
A. ⬆
B. ⬈
C. ⮕
D. ⬇
E. ⬅

C

A small ball attached to the end of a string experiences a uniform circular motion on a horizontal frictionless table. In order to keep the ball moving in a circle, the string must apply force on the ball toward the center of the circle. Which of the following refers to a reaction force?
A. The force of gravity pulling down.
B. The normal force pushing up.
C. The force applied by the ball on the table.
D. The force applied by the ball on the string.
E. The force applied by the table on the ball.

D

An object travels in a circular path of radius, r, at a constant speed, v. What happens to the object's acceleration if the circle's radius is doubled and the speed stays unchanged?
A. It doubles.
B. It quadruples.
C. It is cut in half.
D. It is cut into a quarter.
E. It stays unchanged.

C

An object travels in a circular path of radius, r, at a constant speed, v. What happens to the object's acceleration if the speed is doubled and the radius stays unchanged?
A. It doubles.
B. It quadruples.
C. It is cut in half.
D. It is cut into a quarter.
E. It stays unchanged.

B

An object travels in a circular path of radius, r, at a constant speed, v. What happens to the object's acceleration if the circle's radius is quadrupled and the speed is doubled?
A. It doubles.
B. It quadruples.
C. It is cut in half.
D. It is cut into a quarter.
E. It stays unchanged.

E

An object moves at a constant acceleration, a, in a circular path of radius, r. Which of the following is the object's velocity?
A. a ⋅ r
B. ᵃ⁄ᵣ
C. ʳ⁄ₐ
D. sqrt(a ⋅ r)
E. sqrt(ᵃ⁄ᵣ)

D

An object moves around a circular path at a constant speed and makes five complete revolutions in 20 seconds. What is the period of rotation?
A. 5 seconds
B. 10 seconds
C. 4 seconds
D. 20 seconds
E. 15 seconds

C

An object moves around a circular path at a constant speed and makes ten complete revolutions in 5 seconds. What is the frequency of rotation?
A. 2 Hz
B. 4 Hz
C. 6 Hz
D. 10 Hz
E. 20 Hz

A

An object rotates with a period of 10 seconds. How many revolutions will it make in 25 seconds?
A. 10
B. 15
C. 5
D. 2.5
E. 2

D

An object rotates with a frequency of 300 Hz. How many revolutions will it make in 15 seconds?
A. 1000
B. 1500
C. 2000
D. 3500
E. 4500

E

An object rotates with a period of 0.5 seconds. What is the frequency of rotations?
A. 1 Hz
B. 1.5 Hz
C. 2 Hz
D. 2.5 Hz
E. 3 Hz

C

An object rotates with a frequency of 50 Hz. What is the period of rotations?
A. 0.02 seconds
B. 0.15 seconds
C. 0.25 seconds
D. 0.05 seconds
E. 0.03 seconds

A

A ball of mass, m, moves at a constant speed, v, in a circular path with a radius, R. Which of the following represents the net force applied on the ball?
A. mvR
B. ᵐᵛ⁄R
C. ᵐᵛ²⁄R
D. ᵛ²⁄R
E. R⁄ₘᵥ

C

An object of mass, m, moves at a constant speed, v, around a circular path of radius, r. The net force applied to the object is F. What happens to the net force if the speed is doubled and the radius remains the same?
A. It doubles.
B. It quadruples.
C. It stays the same.
D. It is cut in half.
E. It is cut into a quarter.

B

An object of mass, m, moves at a constant speed, v, around a circular path of radius, r. The net force applied to the object is F. What happens to the net force if speed is doubled and radius is quadrupled?
A. It doubles.
B. It quadruples.
C. It stays the same.
D. It is cut in half.
E. It is cut into a quarter.

C

A ball of mass, m, is attached to a light string that moves at a constant speed, v, in a vertical circle with a radius, R. Which of the following is true about the magnitude of the net force at the top of the circle compared to that at the bottom of the circle?
A. The net force at the top of the circle is greater than at the bottom of the circle.
B. The net force at the top of the circle is less than at the bottom of the circle.
C. The net force is zero at all points around the circle.
D. The net force at the top of the circle is equal to the net force at the bottom of the circle.

D

A rollercoaster car moves on a track with one section that is a vertical circular loop of radius, R. When the car is at the top of the loop, it just maintains contact with the track. What is the car's acceleration?
A. g upward
B. 0.5 g upward
C. Zero
D. 0.5 g downward
E. g downward

E