Find the dimensions of: 1. Angular speed . 2. Angular acceleratio… - Vidyadip

Question

Find the dimensions of:

Angular speed $\omega.$
Angular acceleration $\alpha.$
Torque $\tau$ and
Moment of interia I.

Some of the equations involving these quantities are

$\omega=\frac{\theta_2-\theta_1}{\text{t}_2-\text{t}_1},\alpha=\frac{\omega_2-\omega_1}{\text{t}_2-\text{t}_1},\tau=\text{F.r}$ and $\text{I = mr}^2.$

The symbols have standard meanings.

✓

Answer

Angular speed $\omega=\frac{\theta}{\text{t}}=[\text{M}^0\text{L}^0\text{T}^{-1}]$
Angular acceleration $\alpha=\frac{\omega}{\text{t}}=\frac{\text{M}^0\text{L}^0\text{T}^{-1}}{\text{T}}=[\text{M}^0\text{L}^0\text{T}^{-2}]$
Torque $\tau=\text{Fr}=[\text{MLT}^{-2}][\text{L] = [ML}^2\text{T}^{-2}]$
Moment of inertia $=\text{Mr}^2=[\text{M}][\text{L}^2]=[\text{ML}^2\text{T}^0]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Introduction to Physics→Introduction to Physics — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Estimate the temperature of the gas at constant pressure at which its speed at $27^{\circ} C$ is $\text {r.m.s.}$ The velocity will double.

Find the value of one light year in giga metre.

The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. Choose the correct entries in the brackets below :
(a) (A/B) lives closer to the school than (B/A)
(b) (A/B) starts from the school earlier than (B/A)
(c) (A/B) walks faster than (B/A)
(d) A and B reach home at the (same/different) time
(e) (A/B) overtakes (B/A) on the road (once/twice).

If the mass of the sun is $2 \times 10^{30} kg$, the distance of the earth from the sun is $1.5 \times 10^{11} m$ and period of revolution of the earth around the sun is one year ( $=365.3$ days), calculate the value of gravitational constant.

The displacement of a progressive wave is represented by $y = A \sin (\omega t - kx )$, where x is distance and t is time. Write the dimensional formula of
i. $\omega$ and
ii. k .

It is proposed to move a particle in simple harmonic motion on a rough horizontal surface by applying an external force along the line of motion. Sketch the graph of the applied force against the position of the particle. Note that the applied force has two values for a given position depending on whether the particle is moving in positive or negative direction.

The pressure measured by a constant volume gas thermometer is 40kPa at the triple point of water. What will be the pressure measured at the boiling point of water (100^°C)?

Find the area enclosed by the curve $\text{y}=\sin\text{x}$ and the X-axis between $\text{x}=0$ and $\text{x}=\pi.$

The first overtone frequency of a closed organ pipe P₁ is equal to the fundamental frequency of an open organ pipe P₂. If the length of the pipe P₁ is 30cm, what will be the length of P₂?

The yield point of a typical solid is about 1%. Suppose you are lying horizontally and two persons are pulling your hands and two person are pulling your legs along your own length. How much will be the increase in your length if the strain is 1%? Do you think your yield point is 1% or, much less than that?