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Chapter 9: Problem 11

When a disc rotates with uniform angular velocity, which of the following is not true? [NCERT Exemplar] (a) The sense of rotation remains same (b) The orientation of the axis of rotation remains same (c) The speed of rotation is non-zero and remains same (d) The angular acceleration is non-zero and remains same

Short Answer

Expert verified
Option (d) is not true.

Step by step solution

01

Understanding Uniform Angular Velocity

When a disc rotates with uniform angular velocity, it means the disc is rotating at a constant rate around a fixed axis, without speeding up or slowing down.
02

Evaluating Option (a)

Option (a) states that the sense of rotation remains the same. With uniform angular velocity, the disc continues to rotate in the same direction, so option (a) is true.
03

Evaluating Option (b)

Option (b) states that the orientation of the axis of rotation remains the same. Uniform angular velocity implies that there is no change in the axis, confirming that option (b) is true.
04

Evaluating Option (c)

Option (c) says the speed of rotation is non-zero and remains the same. Since the velocity is uniform, the speed does not change, making this statement true under uniform angular velocity.
05

Evaluating Option (d)

Option (d) suggests that angular acceleration is non-zero and remains the same. For uniform angular velocity, the disc does not accelerate, meaning the angular acceleration is zero. Therefore, option (d) is not true.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angular Motion
Angular motion involves the rotation of an object around a fixed axis. Imagine a spinning disc or a child鈥檚 merry-go-round. Each point on the disc moves in a circular path. The motion is characterized by an angle through which a point on the disc moves, measured in radians. Here鈥檚 a simple breakdown:
  • Axis of Rotation: An imaginary line that the object rotates around.
  • Angular Displacement: The angle through which a point or a line has been rotated in a specified sense about a specified axis.
  • Angular Velocity: This measures how fast something rotates. It is usually given in radians per second.
Understanding angular motion helps in analyzing everything from gears in a clock to the rotations of planets in the solar system. In many cases, the motion is periodic, which means it repeats itself after some time.
Constant Speed
Constant speed in the context of rotational motion means that an object, like a rotating disc, completes equal turns in equal intervals of time. Imagine watching the second hand on a clock; its speed remains unchanged. This is crucial for devices like fans or wheels where a steady speed is necessary for smooth operation. Key aspects include:
  • Uniform Angular Velocity: The rate of rotation doesn't change over time.
  • Fixed Frequency: The number of complete rotations per unit time remains the same.
  • Constant Momentum: The rotational momentum of the object is stable.
The importance of constant speed becomes evident when precision in timing or movement is necessary, such as in mechanical watches or vehicle wheels.
Rotational Dynamics
Rotational dynamics deals with the effect of torques and forces on rotational motion. It is analogous to linear dynamics but focuses on rotating systems. If you鈥檝e ever spun a ball on a string, you have seen rotational dynamics in action. The principles here include:
  • Torque: The force that causes an object to rotate. It鈥檚 the rotational equivalent of linear force.
  • Moment of Inertia: A measure of an object's resistance to changes in its rotation.
  • Angular Momentum: The rotational equivalent of linear momentum, which is conserved in a closed system.
Understanding rotational dynamics is essential for designing anything that involves rotation, like engines or spinning rides at amusement parks, as it informs how these objects will behave under different forces.
Angular Acceleration
Angular acceleration measures how quickly the angular velocity of an object changes with time. Consider a car wheel starting from rest and increasing speed - it initially accelerates when the driver steps on the gas pedal. Angular acceleration, \( \alpha \), can be calculated as: \[\alpha = \frac{\Delta \omega}{\Delta t}\]where \( \Delta \omega \) is the change in angular velocity and \( \Delta t \) is the time it takes for that change. Important points include:
  • Zero Angular Acceleration: Indicates that the object rotates with uniform angular velocity.
  • Positive Angular Acceleration: Implies the object is speeding up.
  • Negative Angular Acceleration: Implies the object is slowing down.
The concept is pivotal in understanding scenarios such as car braking and how efficiently bikes can accelerate or decelerate.

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Most popular questions from this chapter

From a circular dise of radius \(R\) and mass \(9 M\), a small disc or radius \(R / 3\) is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the dise and passing through \(O\) is [IIT JEE 2005] (a) \(4 \mathrm{MR}^{2}\) (b) \(\frac{40}{9} \mathrm{MR}^{2}\) (c) \(10 \mathrm{MR}^{2}\) (d) \(\frac{37}{9} M R^{2}\)

Two wheels \(A\) and \(B\) are mounted on the same axle. Moment of inertia of \(A\) is \(6 \mathrm{kgm}^{2}\) and it is rotating at \(600 \mathrm{rpm}\) when \(B\) is at rest. What is moment of inertia of \(B\), if their combined speed is 400 rpm? (a) \(8 \mathrm{~kg} \mathrm{~m}^{2}\) (b) \(4 \mathrm{~kg} \mathrm{~m}^{2}\) (c) \(3 \mathrm{~kg} \mathrm{~m}^{2}\) (d) \(5 \mathrm{~kg} \mathrm{~m}^{2}\)

A thin uniform rod of length \(l\) and mass \(m\) is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is w. Its centre of mass rises to a maximum height of (a) \(\frac{\mathrm{lcs}}{\mathbf{6 g}}\) (b) \(\frac{l^{2} \omega^{2}}{2 g}\) (c) \(\frac{P^{2} \mathrm{e}^{2}}{6 \mathrm{~g}}\) (d) \(\frac{l^{2} \omega^{2}}{3 g}\)

Assertion The velocity of a body at the bottom of an inclined plane of given height is more when it slides down the plane compared to when it rolls down the same plane. Reason In rolling down, a body acquires both, kinetic energy of translation and kinetic energy of rotation.

Four 2 kg masses are connected by \(\frac{1}{4} \mathrm{~m}\) spokes to an axle. A force of \(24 \mathrm{~N}\) acts on a lever \(1 / 2 \mathrm{~m}\) long to produce angular acceleration \(\alpha\). The magnitude of \(\alpha\) in \(\mathrm{rad} \mathrm{s}^{-2}\) is (a) 24 (b) 12 (c) 6 (d) 3
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