Angular Speed Questions

---

Very Short Answers Questions [1 Mark Questions]

Ques. What is the relationship between angular speed and linear speed?

Ans. Let v and ω be the linear and angular speed of a body respectively rotating in a circle of radius r, then the relation between the angular speed and linear speed is given by

ω = v / r

Ques. Is angular speed a vector or scalar quantity?

Ans. Angular speed is a scalar quantity.

Ques. What is the value of angular speed for 1 revolution?

Ans. The distance covered by a body in one revolution is, θ = 2π

Let, t be the time taken to complete one revolution, then angular speed is given by

ω = θ / t = 2π / t

Ques. The rate at which the angular displacement changes with time is called

1. Angular acceleration
2. Angular velocity
3. Angular distance
4. None of the above

Ans. The correct answer is b. Angular velocity

Explanation: The rate at which the angular displacement changes with time is called angular velocity.

Ques. The SI unit of angular speed is

1. N m
2. rad/s²
3. rad/s
4. rad

Ans. The correct answer is c. rad/s

Explanation: The angular speed can be calculated by the distance traveled by a body in terms of revolutions or rotations per unit of time. Its SI unit is rad/s.

---

Short Answers Questions [2 Marks Questions]

Ques. If a ball is traveling in a circle of diameter 20 m with a velocity of 40 m/s, then calculate the angular velocity of the ball.

Ans. Given

• The radius of the circular path, r = diameter / 2 = 20/2 = 10 m
• The linear velocity of the ball, v = 40 m/s

The relationship between angular velocity and linear velocity is given by

ω = v/r = 40/10 = 4 rad/s

Ques. A car tyre of diameter 0.6 m makes 9.3 revolutions per second. Calculate the angular speed of the car.

Ans. Given

• The radius of the tire of the car, r = 0.6/2 = 0.3 m
• The frequency of the revolution, f = 9.3 revolutions per second

The angular speed of the car is given by

ω = 2πf = 2 x 3.14 x 9.3 = 58.4 rad/s

Ques. What will be the angular velocity of a rotating top if it travels π radians in a third of a second?

Ans. Given

• Angular displacement, θ = π radians
• Time taken, t = 1/3 second

Angular velocity is given by

ω = θ/t = π/(1/3) = 3π rad/s

Ques. What is the similarity and difference between Angular Speed and Angular Velocity?

Ans. The similarity between angular speed and angular velocity is that the SI unit of both the quantity is radian per second.

The difference between angular speed and angular velocity is that angular velocity is a vector quantity, while angular speed is a scalar quantity.

Also read:

---

Long Answers Questions [3 Marks Questions]

Ques. A car wheel of radius 30 inches rotates at 10 revolutions per second on the highway. Find the angular speed of the tyre.

Ans. Given

• The frequency of the car wheel, f = 10 revolutions per second
• The radius of the car wheel, r = 30 inches

Angular speed is equal to the magnitude of angular velocity i.e.

Angular speed, ω = 2πf

Where f is the frequency of the revolution.

Therefore

Angular speed, ω = 2 x 3.14 x 10 = 62.8 rad/s

Ques. What is the angle between the Acceleration Vector and Velocity Vector?

Ans. The angle between the velocity and acceleration vector varies depending on the following different forms of motion.

• If there is circular motion, then the angle between the acceleration vector and velocity vector is 90°

• Depending on whether the speed of a body is increasing or decreasing in a linear motion, the angle between the acceleration vector and velocity vector may be 0° or 180°.

Ques. A car is moving at a speed of 72 km/hr. The diameter of its wheel is 0.52 m. If the wheels are stopped in 20 rotations by applying brakes, then what will be the angular retardation produced by the brakes?

Ans. Given

• Speed of the car, v = 72 km/h = 72 x 5/18 = 20 m/s
• The radius of the wheel, r = 0.52 /2 = 0.26 m
• Angular distance covered by the car, s = 20 rotations

Circumference of one rotation = 2πr = 2 x 3.14 x 0.26 = 1.63 m

Therefore, the total distance covered in 2 rotations = 20 x 1.63 = 32.65 m

Also, the initial angular speed, ωi = v/r = 20/0.26 = 76.92 rad/s

Using the equation of rotational motion, we have

ω²_f = ω²_i + 2as

⇒ Angular acceleration, a = ( ω²_f - ω²_i)/2s

⇒ a = (0 - 76.922) / (2 x 32.65)

---

Very Long Answers Questions [5 Marks Questions]

Ques. Two discs are rotating about their axes, normal to the discs and passing through the center of the discs. Disc D₁ has a 2 kg mass, 0.2 m radius, and an initial angular speed of 50 rad/s. Disc D₂ has a 4 kg mass, 0.1 m radius, and an initial angular speed of 200 rad/s. The two discs are brought into contact face-to-face with their axes of rotation coincidentally. Find the final angular speed of the system.

Ans. Given

• The mass of the first disc, m₁ = 2 kg
• The radius of the first disc, r₁ = 0.2 m
• The angular speed of the first disc, ω₁ = 50 rad/s
• The mass of the second disc, m₂ = 4 kg
• The radius of the second disc, r₂ = 0.1 m
• The angular speed of the second disc, ω₂ = 200 rad/s

The moment of inertia of the first disc is given by

I₁ = m₁r₁² / 2 = (2 x 0.22) / 2 = 0.04 kg m²

The moment of inertia of the second disc is given by

I₂ = m₂r₂² / 2 = (4 x 0.12) / 2 = 0.02 kg m²

When they are brought in contact, then the final angular speed of the system is given by

ω_f = (I₁ω₁ + I₂ω₂) / (I₁ + I₂)

⇒ ω_f = (0.04 x 50 + 0.02 x 200) / (0.04 + 0.02)

⇒ ω_f = (2 + 4) / (0.06) = 6 / 0.06

⇒ ω_f = 100 rad/s

Ques. A constant torque of 1000 N m turns a wheel of a moment of inertia 200 kg m² about an axis through its center. Calculate the angular speed after 3 seconds.

Ans. Given

• Initial angular speed, ω_i = 0
• Torque applied to turn the wheel, ???? = 1000 N m
• Moment of inertia of the wheel, I = 200 kg m²

From equations of rotational motion, the final angular speed is given by

ω_f = ω_i + at

Where a is the constant angular acceleration and it is also given by

a = ???? / I = 1000 / 200 = 5 rad/s²

Therefore, the angular speed after 3 seconds will be

ω_f = 0 + (5 x 3)

⇒ ω_f = 15 rad/s

Ques. Earth takes a whole year (365 days) to complete a single revolution around the sun. Calculate the angular speed with which the Earth is rotating around the sun.

Ans. Given, the time taken by the earth to complete one revolution is t = 365 days

⇒ t = 365 x 24 x 60 x 60 = 31536000 seconds

Angular distance covered by the earth to complete one revolution, θ = 2π

Therefore, the angular speed of the earth is given by

ω = θ / t

⇒ ω = 2π / 31536000

⇒ ω = 2 x 3.14 / 31536000 = 6.28 / 31536000

⇒ ω = 1.99 x 10^-7 rad/s

---

Previous Year Questions

1. Extraction of metal from the ore cassiterite involves...[JEE Advanced 2011]
2. Commonly used vectors for human genome sequencing are...[NEET UG 2014]
3. Interfascicular cambium and cork cambium are formed due to​..
4. Pneumotaxic centre is present in​...[UP CPMT 2007]
5. Reaction of HBr with propene in the presence of peroxide gives….[NEET UG 2004]
6. Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is...[MHT CET 2016]
7. Which among the following is the strongest acid?...[TS EAMCET 2017]
8. Isopropyl alcohol on oxidation forms​..
9. A vector is not changed if​..
10. Which of the following arrangements does not represent the correct order of the property stated against it?...[JEE Main 2013]

For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates

---

Check-Out: