WorksheetsIntroduction to Circular Motion
Total questions: 93
Worksheet time: 47mins
Which statement best defines circular motion in kinematics?
Motion of a body around a center of rotation
Motion of a body along a straight horizontal line
Motion of a body in random three-dimensional paths
Motion of a body oscillating between two fixed points
Why is circular motion considered two-dimensional?
Its x and y positions change while distance to axis stays constant
Its speed always increases with time in all directions
It requires forces acting only along the vertical axis
It uses only one coordinate to describe its position
A body moves around a circle covering equal arc lengths in equal times. Which conclusion is most justified?
The motion is uniform circular motion by definition
The motion is nonuniform because speed changes direction
The motion is linear because displacement becomes zero
The motion is three-dimensional due to rotation
Which statement best defines angular displacement in circular motion?
The angle an object travels around a center
The distance along a straight line path
The time taken to complete one rotation
The rate of change of linear speed
Which set correctly matches one full revolution to its equivalent angle measures?
360 degrees, 2π radians, about 6.28 radians
180 degrees, π radians, about 3.14 radians
90 degrees, π/2 radians, about 1.57 radians
57.3 degrees, 1 radian, about 1.00 radians
A wheel turns through 114.6 degrees. Approximately how many radians is this angular displacement?
About 2.00 radians
About 1.00 radians
About 3.14 radians
About 6.28 radians
A point on a rotating disk moves along an arc length equal to the disk’s radius. What is the angular displacement in radians?
Exactly 1 radian
Exactly 2 radians
Exactly π radians
Exactly 2π radians
Which equation correctly relates arc length s, radius r, and angular displacement θ when θ is in radians?
s = θ · r
s = θ ÷ r
s = r ÷ θ
s = r + θ
A wheel has a radius of 0.50 m and rotates through an angular displacement of 3.0 rad. What arc length along the rim is traveled?
1.5 m
0.17 m
3.5 m
6.0 m
Why must θ be in radians when using s = θ · r?
Radians make θ dimensionless, giving length units for s
Radians convert r into meters, ensuring correct units
Degrees are always larger, so results would be wrong
Radians and degrees give identical results for any formula
A car moves on a circular track of radius 60 m and completes 25 full laps. Which conversion correctly finds the angular displacement θ in radians?
θ = 25 rev × 2π rad per rev
θ = 25 rev ÷ 2π rad per rev
θ = 60 m × 2π rev per rad
θ = 2π rev ÷ 25 rad per rev
Using θ in radians and radius r, which formula gives the linear distance s traveled along a circular path?
s = θ · r
s = θ ÷ r
s = r ÷ θ
s = θ · r²
For r = 60 m and 25 laps, what is the total distance s traveled? Use π ≈ 3.1416.
s ≈ 9,425 m
s ≈ 1,507 m
s ≈ 3,770 m
s ≈ 28,274 m
A driver completes n laps on a circular track of radius r. Which expression best prevents calculator rounding error when computing s?
s = (2πnr) computed in one step
s = (2πn) rounded to 3.14, then × r
s = (2π) rounded to 6.3, then n × r
s = n × r, then multiply by π twice
Which statement best defines angular velocity for a rotating object?
Ratio of angular displacement to elapsed time
Product of angular displacement and elapsed time
Change of linear displacement per unit time
Number of revolutions divided by radius length
In the formula ω = θ / t, what are the SI units for ω and for θ, respectively?
rad/s and radians
m/s and meters
rev/s and revolutions
N·s and newton·seconds
A wheel completes 50 revolutions in 10 seconds. What is its angular velocity in rad/s? Use 2π rad per revolution.
10π rad/s
5π rad/s
25π rad/s
100π rad/s
A pinwheel makes 100 revolutions in 20 seconds. Which computation correctly finds its angular velocity?
ω = (100 × 2π) rad ÷ 20 s
ω = 100 rev × 20 s ÷ 2π
ω = 20 s ÷ (100 × 2π) rad
ω = (100 ÷ 20) rev × 2π s
Which equation correctly relates tangential (linear) velocity v to angular velocity ω for a point at radius r from the axis of rotation?
v = ω · r
v = r / ω
v = ω / r
v = r · ω²
A wheel has an angular velocity of 6 rad/s. A point on the rim is 0.4 m from the center. What is the point’s tangential speed?
2.4 m/s
1.5 m/s
6.4 m/s
0.24 m/s
Which step explains how v = ω · r is obtained from the definitions of motion?
Use s = θ r and v = s/t with θ = ω t
Differentiate v = r t with respect to time
Set angular momentum equal to linear momentum
Assume ω is measured in revolutions per minute
A vinyl record spins at 33 revolutions in 60 s. What is the angular velocity in rad/s?
3.46 rad/s
0.55 rad/s
6.28 rad/s
2.07 rad/s
Two coins sit on the same spinning record at radii r1 = 0.05 m and r2 = 0.15 m. Which statement is true about their angular velocities?
Both have equal angular velocity
Coin at 0.05 m has larger angular velocity
Coin at 0.15 m has larger angular velocity
Angular velocities cannot be compared
Using v = ωr with ω = 3.46 rad/s, what is the tangential speed of a coin at r = 0.05 m?
0.17 m/s
0.05 m/s
0.35 m/s
0.52 m/s
A second coin is at r = 0.15 m on the same record with ω = 3.46 rad/s. What is its tangential speed?
0.52 m/s
0.17 m/s
0.23 m/s
1.04 m/s
If the record’s speed doubles while radii stay the same, how do the coins’ tangential speeds change?
Both double because v is proportional to ω
Both halve because v is inversely proportional to ω
Only the outer coin changes noticeably
Both stay the same regardless of ω
Which statement best defines frequency in uniform circular motion?
Number of revolutions completed per unit time
Time taken for one complete revolution of motion
Distance covered during each circular revolution
Rate of change of angular displacement vector
A wheel completes 20 revolutions in 5 seconds during uniform circular motion. What is its period T?
0.25 seconds per revolution
4.0 seconds per revolution
0.50 seconds per revolution
2.5 seconds per revolution
Two fans spin with constant speed. Fan A has a period of 0.2 s, and Fan B has a frequency of 2 Hz. Which fan spins faster, and why?
Fan A, because T=0.2 s gives f=5 Hz
Fan B, because 2 Hz equals shorter period
Both, because period and frequency are identical
Fan B, because 2 Hz equals f=0.2 Hz value
Which expression correctly relates angular velocity ω to frequency f for uniform circular motion?
ω = 2πf
ω = f⁄(2π)
ω = 2fπ²
ω = πf⁄2
A wheel spins at 5 revolutions per second. What is its angular velocity? Use π ≈ 3.14.
10.0 rad/s
15.7 rad/s
31.4 rad/s
62.8 rad/s
Which pair of units is correctly matched to the quantity for grade‑level mechanics?
Frequency in revolutions per second; angular velocity in rad/s
Frequency in radians per second; angular velocity in RPM
Frequency in rad/s; angular velocity in revolutions
Frequency in meters per second; angular velocity in Hz
A fan completes 800 revolutions in 40 seconds. What is its rotational frequency in revolutions per second (rps)?
10 rps
15 rps
20 rps
25 rps
A fan completes 800 revolutions in 40 seconds. What is the rotational frequency in revolutions per minute (RPM)?
600 RPM
1,200 RPM
1,000 RPM
1,194 RPM
If the rotational frequency is 20 rps, what is the period of one revolution?
0.05 s
0.2 s
0.02 s
0.5 s
Given a frequency of 20 rps, what is the angular velocity ω in rad/s? (Use ω = 2πf)
62.83 rad/s
94.25 rad/s
125.66 rad/s
157.08 rad/s
Which statement correctly relates period T and frequency f for uniform circular motion?
T equals f squared for all cases
T equals 1 divided by f always
T equals 2π divided by f only
T equals f divided by 2π always
Which statement best defines centripetal acceleration in uniform circular motion?
Acceleration directed radially toward the circle center
Acceleration tangent to the path and forward pointing
Acceleration opposite the motion and speed reducing
Acceleration outward from center due to inertia
A car moves at speed v around a circular track of radius r. Which expression gives the magnitude of its centripetal acceleration?
v squared divided by r
r divided by v squared
v times r squared
r squared divided by v
Which relation correctly links centripetal acceleration to angular velocity ω and radius r for uniform circular motion?
a sub c equals ω squared r
a sub c equals ω divided by r
a sub c equals r divided by ω
a sub c equals ω r squared
An object in circular motion continuously changes direction. Which Newtonian idea explains why a net force must act on it?
Without a net force, motion would remain straight at constant speed
Without a net force, speed must increase to keep turning
With a net force, inertia pushes the object outward
With no forces, velocity vectors cancel around the circle
Which statement best defines centripetal force in uniform circular motion?
Force causing inward radial acceleration
Force pushing outward due to rotation
Force maintaining constant linear velocity
Force opposing motion along the tangent
Using tangential speed v and radius r, which formula gives centripetal acceleration?
ac = v2 / r
ac = r / v2
ac = v / r2
ac = r2 / v
An object of mass m moves in a circle of radius r with angular speed ω. What is the expression for the required centripetal force?
F = m ω2 r
F = m r / ω2
F = ω r2 / m
F = m v2 / r
A 0.50 kg ball moves at 6.0 m/s on a 2.0 m radius circle. What is the centripetal force?
9.0 N toward center
18 N toward center
36 N toward center
6.0 N toward center
A 1200 kg car moves around a curve of radius 60 m at 90 km/h. Convert 90 km/h to m/s.
20 m/s
22 m/s
25 m/s
30 m/s
35 m/s
Using v = ωr, what is the car’s angular velocity when v = 25 m/s and r = 60 m?
0.42 rad/s
0.30 rad/s
0.55 rad/s
0.80 rad/s
1.00 rad/s
Which expression correctly gives centripetal acceleration for the car on the curve?
ac = v r
ac = v2 r
ac = ω2 r
ac = r2 ω
ac = r v
Calculate the centripetal acceleration using ω = 0.42 rad/s and r = 60 m.
4.2 m/s2
7.5 m/s2
10.6 m/s2
15.0 m/s2
22.0 m/s2
What is the centripetal force on the car using F = m v2 / r with m = 1200 kg, v = 25 m/s, r = 60 m?
6,250 N
9,000 N
12,500 N
18,000 N
25,000 N
Which statement best defines torsional moment (torque) in mechanics?
Rotational effect of a force about an axis
Linear push that changes object speed only
Measure of how mass resists linear motion
Energy stored when a spring compresses
A wrench applies a perpendicular force of 20 N at a distance of 0.25 m from a bolt’s axis. What is the torque magnitude on the bolt?
5 N·m
0.8 N·m
50 N·m
80 N·m
Which change increases torque the most when force is perpendicular to the radius?
Doubling the effort arm while keeping force constant
Halving the effort arm while tripling the force
Keeping force and effort arm the same
Reducing both force and effort arm equally
Which expression correctly gives the magnitude of torque when a force F is applied at an angle θ to a lever arm of length r?
τ = F r cos θ
τ = F r sin θ
τ = F r tan θ
τ = F r θ
A driver applies a 25 N force on a steering wheel of radius 0.18 m at 90° to the radius. What is the torque magnitude?
3.2 N·m
4.5 N·m
2.8 N·m
5.6 N·m
Turning the steering wheel to the right corresponds to clockwise rotation about its center. Using the conventional sign for torque, what sign should be assigned to this torque?
Positive, because clockwise is defined as positive
Negative, because clockwise is defined as negative
Zero, because the torque is balanced
Positive, because the force is perpendicular
A wrench of length 0.25 m is used to loosen a bolt. You push with 40 N at an angle of 30° to the wrench (measured from the wrench toward the force). What is the torque magnitude about the bolt?
10 N·m
8.7 N·m
5.0 N·m
6.0 N·m
Which phrase best defines rectilinear motion in mechanics?
Motion along a straight-line path
Motion along a circular curved path
Motion changing in three dimensions
Motion with varying speed directions
Which statement correctly distinguishes distance from displacement?
Distance is path length; displacement is straight-line change
Distance is straight-line change; displacement is path length
Both are vector quantities with directions
Both are scalar quantities without directions
A runner moves 30 m east, then 30 m west along a straight track. What are the distance traveled and the displacement?
Distance 60 m; displacement 0 m
Distance 0 m; displacement 60 m
Distance 30 m; displacement 30 m east
Distance 60 m; displacement 60 m east
On a grid diagram, a red curved path shows the trajectory from an initial point to a final point, and a blue straight arrow connects the same points. What does the blue arrow represent?
The displacement between the two positions
The total distance along the trajectory
The average speed during the motion
The time taken along the trajectory
Which set correctly matches symbols to quantities in rectilinear motion?
xi: initial position; vf: final velocity
xi: final position; vf: initial velocity
vi: final velocity; a: time interval
a: acceleration; Δt: displacement change
An object starts with velocity vi and moves with constant acceleration a for time Δt. Which equation gives its final velocity?
vf = vi + aΔt
vf = xi + viΔt
vf = vi + 1/2 aΔt2
vf = vi − a/Δt
A car moves in a straight line with constant acceleration a. Starting from position xi and initial velocity vi, what expression gives its final position after time t?
xf = xi + vi t + 1/2 a t2
xf = xi + vf t − a t2
xf = xi + vi/t + a t
xf = xi − vi t + a/2 t
When starting a rectilinear motion problem, which step best helps prevent misinterpretation of variables and symbols?
Identify all given data with their units
Assume typical values for missing quantities
Begin simplifying the target equation immediately
Convert only time units to seconds first
You calculate a car’s speed as 20. What is the most appropriate action before reporting your result?
Attach proper units consistent with SI system
Round to the nearest whole number only
Convert all lengths to inches for clarity
Add more significant figures for precision
A car accelerates uniformly from rest to 100 km/h in 6.2 s. What is the correct conversion of 100 km/h to m/s for use in calculations?
27.78 m/s
16.67 m/s
22.22 m/s
36.00 m/s
Using vf = vi + at, what is the car’s acceleration if vi = 0, vf = 27.78 m/s, and t = 6.2 s?
4.48 m/s^2
3.20 m/s^2
6.00 m/s^2
5.90 m/s^2
After finding the acceleration, which kinematics equation correctly gives the distance traveled from rest during the 6.2 s interval?
xf = 21 a t^2
xf = v_f t
xf = v_i t + a
xf=vf2−vi2
Calculate the distance the car travels while accelerating uniformly from 0 to 27.78 m/s in 6.2 s. Use your chosen equation and round to two decimals.
86.11 m
69.00 m
102.50 m
74.22 m
Which type of graph shows an object's position changing with time along one straight line of motion?
Position versus time graph (x vs t)
Velocity versus time graph (v vs t)
Acceleration versus time graph (a vs t)
Force versus time graph (F vs t)
A velocity–time graph is a straight horizontal line at v = 10 m/s for 6 seconds. Which statement best describes the motion?
Constant velocity and zero acceleration throughout
Increasing velocity with positive acceleration
Decreasing velocity with negative acceleration
Changing direction with varying acceleration
On a position–time graph of uniform motion, what physical quantity is given by the slope of the line?
Acceleration of the object
Velocity of the object
Displacement of the object
Elapsed time between events
A straight line on an x–t graph passes through (t = 0 h, x = 0 km) and (t = 1 h, x = 80 km). What is the object’s constant velocity?
20 km/h to the right
40 km/h to the right
60 km/h to the right
80 km/h to the right
Which statement best describes how to predict position using a position–time graph with constant slope?
Extend the line using the same slope
Draw a new curve through latest points
Use the steepest tangent at each point
Average the first and last data positions
A data table shows x increasing by 20 km every 0.25 h. Which conclusion is most justified about the motion?
Velocity is constant and positive
Acceleration is increasing steadily
Speed varies but direction is fixed
Object starts at rest then speeds up
At t = 4 s, what is the speed shown by a velocity–time graph that increases uniformly from 0 m/s at t = 0 s by 2 m/s each second?
6 m/s at four seconds
8 m/s at four seconds
10 m/s at four seconds
12 m/s at four seconds
Which statement best describes what the slope of a velocity–time graph represents?
It represents average speed only
It represents instantaneous velocity
It represents constant distance covered
It represents acceleration of motion
A body’s velocity increases uniformly from 0 to 12 m/s in 6 s. What is the acceleration?
1 m/s^2 upward
2 m/s^2 upward
3 m/s^2 upward
12 m/s^2 upward
Using a velocity–time graph where velocity increases linearly from 0 to 12 m/s over 6 s, what total distance is covered in the 6 s?
18 m by triangular area
24 m by rectangular area
36 m by triangular area
72 m by rectangular area
In an acceleration–time graph, what physical quantity does the area under the curve represent over a time interval?
Change in speed over that interval
Instantaneous speed at a single moment
Total distance traveled by the object
Average position during that interval
A cart experiences a constant acceleration of 2 m/s^2 from t = 0 s to t = 6 s. Using an acceleration–time graph, what is the cart’s change in speed over this interval?
12 m/s increase in speed
6 m/s increase in speed
3 m/s decrease in speed
12 m/s decrease in speed
Two experiments show these acceleration–time graphs for a 6 s interval: Graph A is a horizontal line at 2m/s2 . Graph B is a linearly rising acceleration from 0 to 4m/s2 . Which statement is correct about the change in speed over 6 s?
Both graphs produce the same speed change
Graph A produces a larger speed change
Graph B produces a larger speed change
Neither graph changes the object’s speed
A dog’s position–time graph shows straight-line segments. What does this imply about acceleration within each segment?
Acceleration is constant and nonzero
Acceleration is zero and speed is constant
Acceleration varies but speed is constant
Acceleration is zero while speed varies
From t = 0 s to t = 2 s, the dog’s position increases from 0 m to 3 m. What is the average speed in this interval?
0.33 m/s
1.0 m/s
1.5 m/s
2.0 m/s
Between t = 2 s and t = 4 s, the graph is horizontal at x = 3 m. Which statement best describes the dog’s motion in this interval?
It moves away from the origin steadily
It returns toward the origin slowly
It remains at rest at 3 meters
It accelerates while staying at 3 meters
What is the total distance traveled by the dog from t = 0 s to t = 11 s according to the graph showing final position at 7 m?
7 meters over 11 seconds
5 meters over 10 seconds
9 meters over 12 seconds
11 meters over 7 seconds
Which one-second interval shows the greatest speed on the graph?
From 0 s to 1 s
From 4 s to 10 s
From 10 s to 11 s
From 2 s to 4 s
A velocity–time graph shows lines for bodies A and B. At t = 0 s, A has v = 3 m/s and B has v = 0 m/s. Which body starts from rest?
Body A starts from rest
Body B starts from rest
Both A and B start from rest
Neither A nor B starts from rest
At t = 6 s, both lines on a velocity–time graph intersect at v = 6 m/s. What is the common speed of bodies A and B at that instant?
3 m/s for both bodies
6 m/s for both bodies
9 m/s for both bodies
Zero for both bodies
Using the slope of a velocity–time graph, what is the acceleration of body A if its velocity changes from 3 m/s at t = 0 s to 6 m/s at t = 6 s?
0.2 m/s^2 constant
0.5 m/s^2 constant
1.0 m/s^2 constant
2.0 m/s^2 constant
Body B’s velocity increases from 0 m/s at t = 0 s to 6 m/s at t = 6 s. What is B’s acceleration calculated from the v–t graph?
0.25 m/s^2 upward
0.5 m/s^2 upward
1.0 m/s^2 upward
2.0 m/s^2 upward
Two straight lines on a v–t graph represent bodies A and B. A begins at 3 m/s and B at 0 m/s; at t = 6 s both have 6 m/s. Which reasoning best explains why B’s acceleration is greater than A’s?
B’s line is flatter, so acceleration is smaller
B’s speed decreases slower than A’s speed
B’s line has a steeper slope over equal time
A’s line crosses the time axis sooner than B’s
