Angular Motion Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Write the formula to calculate the velocity in angular motion.

Ans. In angular motion, velocity is termed angular velocity which is defined as the time rate of change of angular displacement (θ). The formula of angular velocity (ω) is given by ω = dθ/dt.

Ques. Angular velocity is a

1. Vector quantity
2. Scalar quantity
3. Dimensionless quantity
4. None of the above

Ans. The correct answer is b. Vector quantity

Explanation: Angular velocity is a vector quantity. The direction of the angular velocity is along the axis of rotation.

Ques. What is the formula to calculate the displacement in linear motion?

1. S = ut + 1/2 at²
2. S = ut x 1/2 at²
3. S = ut² + 1/2 at²
4. S = ut + 1/2 at

Ans. The correct answer is a. S = ut + 1/2 at²

Explanation: From equations of motion, the formula for displacement in linear motion is given by S = ut + 1/2 at²

Ques. How is the relationship between linear speed (v) and angular speed (ω) represented?

1. v = r/ω
2. v = r + ω
3. v = rω
4. v = r²ω

Ans. The correct answer is c. v = rω

Explanation: For a body rotating in a circular path of radius r, the relationship between linear speed (v) and angular speed (ω) represented by v = rω

Ques. What is the formula to calculate the angular acceleration?

1. ɑ = ωr
2. ɑ = dω/dt
3. ɑ = dω + dt
4. ɑ = dω - dt

Ans. The correct answer is b. ɑ = dω/dt

Explanation: The rate at which angular velocity changes over time is known as angular acceleration. The formula for angular acceleration is given by ɑ = dω/dt.

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Short Answers Questions [2 Marks Questions]

Ques. Define angular motion.

Ans. The motion of the body along a curved path with a constant and uniform angular velocity is referred to as angular motion. A runner traveling around a circular path or a car driving around a curve are examples of angular motion.

Ques. Define motion.

Ans. Motion is the phenomenon through which an object changes its position with respect to time. Motion is quantitatively characterized in terms of displacement, distance, velocity, acceleration, speed, and frame of reference of an observer, measuring the change in position of the body relative to that frame as time passes.

Ques. What do you mean by Earth's angular velocity?

Ans. The true angular velocity of the earth for an ordinary day is 15.04108°/means solar hour. This equates to 360°/23 hours, 56 minutes, and 4 seconds. The angular velocity of the earth may alternatively be represented in radians/second form, abbreviated as rad/s, using the formula ωEarth = 2π /T, where T is the earth's sidereal period, which is 23 hours 56 minutes, and 4 seconds.

Ques. Is angular velocity constant in circular motion?

Ans. When an object moves in a circular motion at a constant speed, it experiences linear constant acceleration in order to continue traveling in a circle. The angular velocity is considered to be constant since it sweeps out the same arc length every time. A uniform circular motion can be described as a constant angular velocity in a circle. Yes, the angular velocity of an object traveling in a circular motion is constant.

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Long Answers Questions [3 Marks Questions]

Ques. What is the angular velocity of the hour hand in the clock?

Ans. In 12 hours, the hour hand turns 360 degrees. As a result, the hour hand's angular displacement is 2π and the time taken is 12 x 3600 seconds.

Therefore, the angular velocity of the hour hand in the clock will be,

ω = Δθ / Δt

⇒ ω = 2π / (12 x 3600) = π / 21600 rad/s.

Ques. What is meant by torque? State its difference from the force.

Ans. Torque is the force that may cause an object to twist along an axis. 

• Force is what causes an object to accelerate in linear kinematics. 
• Torque causes angular acceleration. 
• Torque is the rotating equivalent of linear force. 
• The object's axis of rotation is the point at which it rotates. 
• The SI unit for torque is N-m. Torque is the opposite of force in rotational mechanics. 
• The primary comparison between them is the ability of a force to create a twist around an axis.

Ques. What is the angular kinetic energy of a body whose moment of inertia is 800 kg m² and whose angular velocity is 30 rad/s?

Ans. Given

• The moment of inertia of the body, I = 800 kg m²
• The angular velocity of the body, ω = 30 rad/s

The angular kinetic energy of a rotating body is given by

E = (1/2)Iω²

Where

• E is the angular kinetic energy
• I is the moment of inertia
• ω is the angular velocity

On substituting the values, we get

Angular kinetic energy, E = (1/2) x 800 x 30²

⇒ E = 360000 J

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Very Long Answers Questions [5 Marks Questions]

Ques. Write down the main characteristics of angular acceleration.

Ans. The followings are the characteristics of angular acceleration

• Positive angular acceleration occurs when angular velocity rises over time.
• If angular velocity decreases over time, angular acceleration is negative.
• Angular acceleration is an axial vector.
• Since angular velocity is constant in a uniform circular motion, angular acceleration is zero.

Ques. A constant torque of 2000 N m turns a wheel of a moment of inertia 100 kg m² about an axis through its center. Calculate the angular speed after 4 seconds.

Ans. Given

• Initial angular speed, ω_i = 0
• Torque applied to turn the wheel, τ = 2000 N m
• Moment of inertia of the wheel, I = 100 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 = τ / I = 2000 / 100 = 20 rad/s²

Therefore, the angular speed after 3 seconds will be

ω_f = 0 + (20 x 4)

⇒ ω_f = 80 rad/s

Ques. The wheel of a car is rotating at the rate of 1800 revolutions per minute. On pressing the accelerator for 12 seconds, it starts rotating at 3000 revolutions per minute. Calculate the angular acceleration of the wheel.

Ans. Initially, the frequency of the revolution, f_i = 1800 revolutions per minute = 1800 / 60 revolutions per second

⇒ the frequency of the revolution, f_i = 30 revolutions per second

Therefore initial angular velocity of the wheel is given by

ω_i = 2πf_i

⇒ ω_i = 2 x 3.14 x 30 = 188.4 rad/s

Finally, the frequency of the revolution, f_f = 3000 revolutions per minutes = 3000 / 60 revolutions per second

⇒ the frequency of the revolution, f_f = 50 revolutions per second

Therefore final angular velocity of the wheel is given by

ω_f = 2πf_f

⇒ ω_f = 2 x 3.14 x 75 = 314 rad/s

Angular acceleration is given by

a = (ω_f - ω_i) / t

⇒ a = (314 - 188.4) / 12 = 10.47 rad/s²

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