A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along
- \( +j \)
- \( -j \)
- \( +k \)
- \( -k \)
The Correct Option is D
Solution and Explanation
To determine the direction of angular velocity, we use the right-hand rule. If the fan is rotating counterclockwise, the angular velocity vector points along the negative \( k \)-axis, indicating the direction of rotation.
Top Questions on Rotational motion
A tube of length 1m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is \( F \) and the angular velocity of the tube is \( \omega \), then the value of \( \alpha \) is ______ in SI units.
- JEE Main - 2025
- Physics
- Rotational motion
A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{\mathrm{x}}{5}}$ where $\mathrm{x}=$ _______.
- JEE Main - 2025
- Physics
- Rotational motion
If $\overrightarrow{\mathrm{L}}$ and $\overrightarrow{\mathrm{P}}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector $\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t})$. The direction of force is
- JEE Main - 2025
- Physics
- Rotational motion
Which of the following are correct expression for torque acting on a body?
A. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{L}}$
B. $\ddot{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\ddot{\mathrm{r}} \times \ddot{\mathrm{p}})$
C. $\ddot{\tau}=\ddot{\mathrm{r}} \times \frac{\mathrm{d} \dot{\mathrm{p}}}{\mathrm{dt}}$
D. $\ddot{\tau}=\mathrm{I} \dot{\alpha}$
E. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{F}}$
( $\ddot{r}=$ position vector; $\dot{\mathrm{p}}=$ linear momentum; $\ddot{\mathrm{L}}=$ angular momentum; $\ddot{\alpha}=$ angular acceleration; $\mathrm{I}=$ moment of inertia; $\ddot{\mathrm{F}}=$ force; $\mathrm{t}=$ time $)$
Choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- Rotational motion
A wheel of radius $ 0.2 \, \text{m} $ rotates freely about its center when a string that is wrapped over its rim is pulled by a force of $ 10 \, \text{N} $. The established torque produces an angular acceleration of $ 2 \, \text{rad/s}^2 $. Moment of inertia of the wheel is............. kg m².
- JEE Main - 2025
- Physics
- Rotational motion
Questions Asked in KCET exam
- Given, a current carrying wire of non-uniform cross-section, which of the following is constant throughout the length of the wire?
- KCET - 2025
- Current electricity
- If the number of terms in the binomial expansion of \((2x + 3)^n\) is 22, then the value of \(n\) is:
- KCET - 2025
- Binomial theorem
- If \( A = \{ x : x \text{ is an integer and } x^2 - 9 \geq 0 \} \), \[ B = \{ x : x \text{ is a natural number and } 2 \leq x \leq 5 \}, \quad C = \{ x : x \text{ is a prime number} \leq 4 \} \] Then \( (B - C) \cup A \) is:
- KCET - 2025
- Set Theory
- The number of four digit even numbers that can be formed using the digits 0, 1, 2 and 3 without repetition is:
- KCET - 2025
- permutations and combinations
- Which of the following methods of expressing concentration are unitless?
- KCET - 2025
- Expressing Concentration of Solutions