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Relationship Between Linear And Angular Motion - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Equations of Linear Motion and Rotational Motion. is considered one of the most asked concept.

  • 24 Questions around this concept.

Solve by difficulty

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 \omega . Its centre of mass rises to a maximum height of

A rod of length 50 cm is provided at one end. It is raised such that it makes an angle of $30^{\circ}$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal ( in rad s ${ }^{-1}$ ) will be ( $\mathrm{g}=10 \mathrm{~ms}^{-}$ $\left.{ }^2\right)$

A particle of mass $m$ moves along line PC with velocity $\nu$ as shown. What is the angular momentum of the particle about P?

A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6 m. The height of the table from the ground is 0.8 m. If the angular speed of the particle is 12 rad s-1, the magnitude (in kg m2s-1) of its angular momentum about a point on the ground right under the centre of the circle is :

A wheel starting from rest gains an angular velocity of 10 rad/s after uniformly accelerating for 5 sec. The total angle through which it has turned is

A blade of fan of an aeroplane is rotating at the rate of 600 rotations per minutes, then its angular velocity will be equal to:

 

What is the value of linear velocity of $\vec{w}=2 \hat{i}-2 \hat{j}+\hat{k}$ and $\vec{\gamma}=3 \vec{i}-\vec{j}-\vec{k}$

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Concepts Covered - 1

Equations of Linear Motion and Rotational Motion.

 

 

Linear Motion

Rotational Motion

I

If linear acceleration =a=0

Then  u = constant 

and s = u t.

If angular acceleration=$\alpha=0$

Then   w = constant

and  $\theta=\omega \cdot t$

II

If linear acceleration= a = constant

1. $a=\frac{v-u}{t}$
2. $v=u+a t$
3. $s=u t+\frac{1}{2} a t^2$
4. $s=\frac{v+u}{2} * t$
5. $v^2-u^2=2 a s$
6. $S_n=u+\frac{a}{2}(2 n-1)$
 

 

If angular acceleration=$\alpha=$ constant

  1. 1. $\alpha=\frac{\omega_f-\omega_i}{t}$
    2. $\omega_f=\omega_i+\alpha . t$
    3. $\theta=\omega_i \cdot t+\frac{1}{2} \cdot \alpha \cdot t^2$
    4. $\theta=\frac{\omega_f+\omega_i}{2} * t$
    5. $\omega_f^2-\omega_i^2=2 \alpha \theta$
    6. ${\theta_n}=\omega_i+\frac{\alpha}{2}(2 n-1)$

III

If linear acceleration= a $\neq$ constant

1. $v=\frac{d x}{d t}$
2. $a=\frac{d v}{d t}=\frac{d^2 x}{d t^2}$
3. $v . d v=a . d s$

 

If angular acceleration $=\alpha \neq$ constant
1. $\omega=\frac{d \theta}{d t}$
2. $\alpha=\frac{d \omega}{d t}=\frac{d^2 \theta}{d t^2}$
3. $\omega \cdot d \omega=\alpha \cdot d \theta$

 

  • - Relation between linear and angular properties
    1. $\vec{S}=\theta \overrightarrow{\times} \vec{r}$
    2. $\vec{v}=\omega \overrightarrow{\times} \vec{r}$
    3. $\vec{a}=\alpha \overrightarrow{\times} \vec{r}$

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Equations of Linear Motion and Rotational Motion.

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