A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along _______.
- $+\hat{j}$
- $-\hat{j}$
- $+\hat{k}$
- $-\hat{k}$
The Correct Option is D
Solution and Explanation
In the given problem, the ceiling fan is rotating around a fixed axle, and the direction of angular velocity is along the axis of rotation, which is the z-axis.
Using the right-hand rule for angular velocity:
If the fan is rotating counterclockwise (when viewed from above), the direction of the angular velocity vector is along the positive z-axis.
If the fan is rotating clockwise (when viewed from above), the direction of the angular velocity vector is along the negative z-axis. Since the problem does not specify the direction of rotation, but typically, ceiling fans rotate counterclockwise when viewed from below, the direction of angular velocity is along the positive z-axis.
Thus, the correct answer is (D) \( -k \), assuming clockwise rotation.
Top Questions on Angular velocity and its relation with linear velocity
The oxygen molecule has a mass of 5.30 × 10-26 kg and a moment of inertia of 1.94 ×10-46 kg m2 about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.
- CBSE Class XI
- Physics
- Angular velocity and its relation with linear velocity
- A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick?
- CBSE Class XI
- Physics
- Angular velocity and its relation with linear velocity
- A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no slipping.
- CBSE Class XI
- Physics
- Angular velocity and its relation with linear velocity
From a uniform disk of radius R, a circular hole of radius \(\frac{R}{2}\) is cut out. The centre of the hole is at \(\frac{R}{2}\) from the centre of the original disc. Locate the centre of gravity of the resulting flat body.
- CBSE Class XI
- Physics
- Angular velocity and its relation with linear velocity
To maintain a rotor at a uniform angular speed of 200 rad s-1, an engine needs to transmit a torque of 180 N m. What is the power required by the engine ? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.
- CBSE Class XI
- Physics
- Angular velocity and its relation with linear velocity
Questions Asked in KCET exam
- Auxins : Apical dominance : : Gibberellins : .............
- KCET - 2024
- Plant Physiology
- The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free electrons which flow through a given cross-section of the conductor in the time interval \( 0 \leq t \leq 20 \, \text{s} \) is
- KCET - 2024
- Current electricity
- A die is thrown 10 times. The probability that an odd number will come up at least once is:
- KCET - 2024
- Probability
- The incorrect statement about the Hall-Heroult process is:
- KCET - 2024
- General Principles and Processes of Isolation of Elements
- Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:
- KCET - 2024
- Linear Programming Problem