Combined Linear and Angular Kinematics: Master the Motion of Objects

Question 1

A disk rolling without slipping on a horizontal surface. If the disk's linear velocity is 4 m/s and its angular velocity is 2 rad/s, what is the disk's radius?

Accepted Answer

2 m

Answer

3 m

Answer

1 m

Answer

4 m

Question 2

A wheel rolls down a straight path without slipping. Which of the following statements is correct regarding the wheel's motion?

Accepted Answer

The wheel's linear velocity and angular velocity are in the same direction.

Answer

The wheel's translational velocity is zero.

Answer

The wheel's linear velocity and angular velocity are in opposite directions.

Question 3

A car travels around a circular track at constant speed. Which of the following statements is true about its acceleration?

Accepted Answer

The car's acceleration is always towards the center of the track.

Answer

The car's acceleration is zero.

Answer

The car's acceleration is always tangential to the track.

Question 4

A person jumps vertically in the air. At the highest point of their jump, their:

Accepted Answer

Linear velocity is zero and angular velocity may or may not be non-zero.

Answer

Linear velocity is non-zero and angular velocity is zero.

Answer

Linear velocity and angular velocity are both zero.

Question 5

A wheel is rolling along a surface. Which of the following factors does NOT affect its rotational kinetic energy?

Accepted Answer

Its linear velocity.

Answer

Its radius.

Answer

Its mass.

Answer

Its angular velocity.

Question 6

A gymnast performs a somersault in the air. Which of the following quantities is conserved during the somersault?

Accepted Answer

Angular momentum.

Answer

Linear momentum.

Answer

Energy.

Answer

Velocity.

Question 7

Which of the following devices can be used to measure angular velocity?

Accepted Answer

Tachometer.

Answer

Accelerometer.

Answer

Thermometer.

Answer

Force gauge.

Question 8

A car is traveling at a constant speed of 20 m/s and rounds a curve with a radius of 50 m. Determine the car's centripetal force.

Accepted Answer

800 N

Answer

1200 N

Answer

200 N

Answer

400 N

Question 9

A gymnast performs a backflip with an initial angular velocity of 8 rad/s. If the gymnast's moment of inertia is 0.6 kg-m², calculate their rotational power at the instant the flip begins.

Accepted Answer

32 W

Answer

48 W

Answer

16 W

Answer

24 W

Question 10

A gymnast performing a salto in the air has an angular velocity of 5 rad/s and a linear velocity of 10 m/s. What is the gymnast's tangential velocity?

Accepted Answer

5 m/s

Answer

25 m/s

Answer

10 m/s

Answer

15 m/s

Question 11

A car travels around a circular track of radius 50 m at a constant speed of 10 m/s. What is the car's angular velocity?

Accepted Answer

0.2 rad/s

Answer

0.6 rad/s

Answer

0.4 rad/s

Answer

0.8 rad/s

Question 12

A wheel is rotating about a fixed axis with an angular acceleration of 2 rad/s². If the wheel starts from rest, what will be its angular displacement after 5 seconds?

Accepted Answer

25 rad

Answer

100 rad

Answer

12.5 rad

Answer

50 rad

Question 13

A ball is thrown into the air with an initial velocity of 10 m/s at an angle of 30° above the horizontal. What is the ball's velocity at the highest point of its trajectory?

Accepted Answer

5 m/s

Answer

10 m/s

Answer

15 m/s

Answer

20 m/s

Question 14

A skater spins on a circular ice rink with a radius of 5 m. If the skater completes 10 revolutions in 20 seconds, what is their centripetal acceleration?

Accepted Answer

0.5 m/s²

Answer

1.5 m/s²

Answer

2.0 m/s²

Answer

1.0 m/s²

Question 15

A car is traveling on a circular track with a radius of 100 m at a speed of 20 m/s. What is the car's angular momentum about the center of the circle?

Accepted Answer

2000 kg m²/s

Answer

4000 kg m²/s

Answer

3000 kg m²/s

Answer

1000 kg m²/s

Question 16

A person standing on a rotating platform with a radius of 2 m holds a mass of 1 kg at a distance of 1 m from the center. If the platform rotates at 5 rad/s, what is the centripetal force exerted by the person on the mass?

Accepted Answer

25 N

Answer

12.5 N

Answer

100 N

Answer

50 N

Question 17

A spinning top has a moment of inertia of 0.005 kg m² and an angular velocity of 10 rad/s. What is the kinetic energy of the spinning top?

Accepted Answer

0.25 J

Answer

0.125 J

Answer

1 J

Answer

0.5 J

Question 18

A dancer performs a pirouette on one toe with an angular acceleration of 4 rad/s². If the dancer starts from rest and completes the pirouette in 2 seconds, what is the dancer's final angular velocity?

Accepted Answer

8 rad/s

Answer

16 rad/s

Answer

4 rad/s

Answer

12 rad/s

Question 19

A wheel with a radius of 0.5 m rolls down an inclined plane of angle 30°. If the wheel starts from rest, what is its linear velocity at the bottom of the plane?

Accepted Answer

2.45 m/s

Answer

4.9 m/s

Answer

1.23 m/s

Answer

3.67 m/s