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Relationship Between Linear And Angular Motion - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

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

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

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   \omega = constant

and  \theta = \omega.t

II

If linear acceleration= a = constant

  1. a = \frac{v-u}{t} 

  2. v=u+at

  3. s= ut +\frac{1}{2}at^{2}

  4. s=\frac{v+u}{2}*t

  5. v^{2}-u^{2}=2as

  6.  

S_{n}= u+\frac{a}{2}(2n-1)

 

If angular acceleration=

  1. \alpha = \frac{\omega_f - \omega_i}{t}

  2. \omega_f=\omega_i+\alpha.t

  3. \theta = \omega_i.t+\frac{1}{2}.\alpha.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}(2n-1)

III

If linear acceleration= a \neq constant

  1. v = \frac{dx}{dt}

  2. a = \frac{dv}{dt} = \frac{d^2x}{dt^2}

  3. v.dv = a.ds

 

If angular acceleration=\alpha \neq constant

  1. \omega = \frac{d\theta}{dt}

  2. \alpha = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2}

  3. \omega.d\omega = \alpha.d\theta

 

  • Relation between linear and angular properties

                 1. \vec{S}=\vec{\theta \times \vec{r}}

                 2. \vec{v}=\vec{\omega \times \vec{r}}

                 3. \vec{a}=\vec{ \alpha \times \vec{r}}

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Equations of Linear Motion and Rotational Motion.

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