Linear Velocity Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. The dimension formula of the linear velocity is

1. [M L T^-1]
2. [M² L² T⁰]
3. [M⁰ L T^-1]
4. [M⁰ L^-1 T]

Ans. The correct answer is c. [M⁰ L T^-1]

Explanation: The linear velocity of a body is given by linear displacement per unit time. Therefore its dimensional formula is [M0 L T-1].

Ques. A radial component of a particle is nothing but a component at which the centripetal component of the particle is always parallel to the particle’s velocity.

1. True
2. False

Ans. The correct answer is b. False

Explanation: The tangential component of the particle is one in which the centripetal component of the particle is parallel to the velocity of the particle.

Ques. Linear velocity is a

1. scalar quantity
2. vector quantity
3. pseudo-quantity
4. dimensionless quantity

Ans. The correct answer is b. vector quantity

Explanation: Since linear velocity is defined in terms of both direction and magnitude, therefore it is a vector quantity.

Ques. A body is moving with respect to a stationary frame, its motion can be called

1. Parabolic
2. Relative
3. Circular
4. Absolute

Ans. The correct answer is d. Absolute

Explanation: Absolute motion is defined as motion with regard to a stationary frame. Relative motion occurs in relation to a moving frame of reference.

Ques. What is the SI unit of linear velocity?

Ans. The SI unit of linear velocity is meters per second (m/s).

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Short Answers Questions [2 Marks Questions]

Ques. What is angular velocity?

Ans. Angular velocity is defined as the vector measure of the rotation rate, which relates to how fast an object rotates or revolves relative to another point.

The time rate at which an object rotates or circles around an axis is defined as its angular velocity. It is denoted by ω.

Ques. What is linear velocity?

Ans. The rate of change of displacement with respect to time when an object moves along a straight path is defined as linear velocity.

Ques. What is the formula for linear velocity?

Ans. The linear velocity of an object is determined by the distance it travels in relation to the time it takes. The formula for linear velocity is given by

v = x/t

Where

• v is the linear velocity
• x is the linear displacement of the body
• t is the time in which displacement takes place.

Ques. What is constant linear velocity?

Ans. If a body moves at a constant speed without changing direction, it is said to have a constant linear velocity.

Ques. Define angular displacement.

Ans. The angular displacement of a physical body, also known as the angle of rotation, rotational displacement, or rotary displacement, is the angle at which the body rotates around a center or axis of rotation.

Ques. What is the relation between linear speed and linear velocity?

Ans. The derivative of position with respect to the time function is the linear velocity. Linear velocity is the absolute value of linear speed.

Ques. What is the relation between linear velocity and angular velocity?

Ans. The relation between the linear velocity and angular velocity is given by

v = rω

Where

• v is the linear velocity of the body
• ω is the angular velocity of the body
• r is the radius of the circular path

Ques. Define average velocity.

Ans. Average velocity is defined as the change in the position or displacement of a particle divided by the time interval in which the displacement occurs.

The SI unit of average velocity is meters per second (ms-1).

Ques. Which device is used to measure the speed of the vehicle?

Ans. A speedometer is used in vehicles to measure their speed. It measures the instantaneous speed or magnitude of the instantaneous velocity i.e. speed of the vehicles at a specific instant of time.

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Long Answers Questions [3 Marks Questions]

Ques. Determine the linear velocity of a point rotating at an angular velocity of 12π radians per second at a distance of 8 centimeters from the center of the rotating object.

Ans. Given

• Angular velocity of the object, ω = 12π rad/s
• Radius of the circular path, r = 8 cm = 8 x 10^-2 m

The relation between the linear velocity and angular velocity is given by

v = rω

Where

• v is the linear velocity of the body
• ω is the angular velocity of the body
• r is the radius of the circular path

On substituting the values, we get

v = 8 x 10^-2 x 12π

⇒ v = 3.01 m/s

Ques. Calculate the linear velocity of the tip of the second switch of length 0.02 meters.

Ans. The time period of the tip of the second of a clock is, T = 60 s

The angular velocity of the tip of the second is given by

ω = 2π/T

On substituting the value, we get

Angular velocity, ω = 2π/60

⇒ ω = 0.104 rad/s

The relation between linear velocity and angular velocity is given by

v = rω

Where r is the radius of the circular path, r = 0.02 m (Given)

Therefore,

Linear velocity, v = 0.02 x 0.104 = 0.0021 m/s

Ques. Calculate the angular velocity and linear velocity of the tip of minutes hand of length 10 cm.

Ans. The period of the tip of the minute's hand of a clock is, T = 60 minute = 3600 s

The angular velocity of the tip of the second is given by

ω = 2π/T

On substituting the value, we get

Angular velocity, ω = 2π/3600

⇒ ω = 1.745 x 10^-3 rad/s

The relation between linear velocity and angular velocity is given by

v = rω

Where r is the radius of the circular path, r = 10 cm = 0.1 m (Given)

Therefore,

Linear velocity, v = 0.1 x 1.745 x 10^-3 = 1.745 x 10^-4 m/s

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Very Long Answers Questions [5 Marks Questions]

Ques. What is the difference between linear velocity and angular velocity?

Ans. The following are the differences between linear velocity and angular velocity

Ques. A runner is running around a rectangle track with length = 30 meters and width = 15 meters. He travels around the rectangle track twice, finally running back to the starting point. If the total time he takes to run around the track is 100 seconds, determine average speed and average velocity.

Ans. Given

• Length of the rectangular track, l = 30 m
• Width of the rectangular track, w = 15 m

Perimeter of the track = 2(30 + 15) = 90 m

Since the runner moves 2 times around the track, the distance traveled by the runner will be equal to two times the perimeter of the track i.e.

Total distance traveled, S = 2(perimeter of the track) = 2 x 90 = 180 m

The average speed of the runner = total distance traveled / total time

⇒ Average speed = 180 / 100 = 1.8 m/s

Since the runner finally reaches the same point, his net displacement will be zero. Therefore

Average velocity = net displacement / total time = 0

Ques. A uniform bar AB of length 50 cm rotates anticlockwise about A with constant angular speed. At the instant shown in the figure, the linear speed vc of the center of mass C is 7.5 cm/s.

1. What are the angular speed and angular velocity of the bar?
2. What is the linear velocity at point B?
3. What is the acceleration of the center of mass?

Ans. Given

• The linear velocity of the bar at C, vc = 7.5 cm/s
• Length of the bar, r = 50 cm

1. The angular speed of the bar is given by

ω = v_c/(r/2)

On substituting the values, we get

ω = 7.5/(50/2) = 0.3 rad/s

Angular velocity, \(\vec{\omega}\) = (0.3 rad/s)\(\hat{k}\)

2. The linear velocity of the bar at B is given by

v_B = r_ABω

On substituting the values, we get

v_B = 50 x 0.3 = 15 cm/s

100. We have, r_CM = r_AC = 50/2 = 25 cm

Now as the angular velocity is constant, therefore angular acceleration is zero. The only acceleration is radial acceleration i.e.

ar = ω²r = 0.3² x 25 = 2.25 cm/s²

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