TYPE OF MOTION IN DETAILS

Types of Motion in Detail: Explanation with CBSE Numerical Context

Understanding the types of motion is not only theoretical but also forms the basis for solving many numerical problems asked in CBSE Class 9 Physics exams. Here’s a detailed explanation of the types of motion with a focus on numerical problems often encountered in exams.

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1. Linear Motion (Rectilinear Motion)

Linear motion involves movement in a straight line, and it is categorized as uniform or non-uniform motion.

Key Equations for Linear Motion:

These equations of motion are vital for solving CBSE numericals:

1. v=u+atv = u + at
2. s=ut+12at2s = ut + \frac{1}{2}at^2
3. v2=u2+2asv^2 = u^2 + 2as
4. s=(u+v)2ts = \frac{(u + v)}{2}t

Here:

• uu: Initial velocity (m/s\text{m/s})
• vv: Final velocity (m/s\text{m/s})
• aa: Acceleration (m/s2\text{m/s}^2)
• tt: Time (s\text{s})
• ss: Displacement (m\text{m})

Examples of CBSE Numericals:

a. Uniform Motion Example:
Question (CBSE 2020):
A car travels 60 km in 2 hours. Find its average speed.
Solution:
Average speed =Total distanceTotal time= \frac{\text{Total distance}}{\text{Total time}}

=60 km2 hours=30 km/h= \frac{60 \, \text{km}}{2 \, \text{hours}} = 30 \, \text{km/h}

b. Non-Uniform Motion Example:
Question (CBSE 2019):
A car starts from rest and accelerates uniformly at 2 m/s22 \, \text{m/s}^2 for 5 seconds. Find the distance covered by the car.
Solution:
Using s=ut+12at2s = ut + \frac{1}{2}at^2:

s=0+12(2)(5)2=12(2)(25)=25 ms = 0 + \frac{1}{2}(2)(5)^2 = \frac{1}{2}(2)(25) = 25 \, \text{m}

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2. Circular Motion

Circular motion involves the movement of an object along a circular path. Speed may remain constant, but the direction changes continuously.

Key Concepts:

1. Angular Displacement (θ\theta): Angle subtended at the center.
2. Angular Velocity (ω\omega): Rate of change of angular displacement.
   ω=θt\omega = \frac{\theta}{t}
3. Centripetal Force: F=mv2rF = \frac{mv^2}{r}, where:
   • mm: Mass of the object
   • vv: Velocity
   • rr: Radius of the circle

Examples of CBSE Numericals:

a. Uniform Circular Motion Example:
Question (CBSE 2021):
An object of mass 5 kg5 \, \text{kg} is moving in a circular path of radius 2 m2 \, \text{m} with a velocity of 4 m/s4 \, \text{m/s}. Find the centripetal force acting on the object.
Solution:
Using F=mv2rF = \frac{mv^2}{r}:

F=5(4)22=5(16)2=40 NF = \frac{5(4)^2}{2} = \frac{5(16)}{2} = 40 \, \text{N}

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3. Periodic Motion

Periodic motion repeats itself at regular intervals.

Key Concepts:

1. Time Period (TT): Time taken for one complete cycle.
2. Frequency (ff): Number of cycles per second. f=1Tf = \frac{1}{T}

Examples of CBSE Numericals:

a. Pendulum Motion Example:
Question (CBSE 2018):
A simple pendulum completes 20 oscillations in 25 seconds. Find its frequency and time period.
Solution:

Frequency,f=Number of oscillationsTotal time=2025=0.8 Hz\text{Frequency}, f = \frac{\text{Number of oscillations}}{\text{Total time}} = \frac{20}{25} = 0.8 \, \text{Hz} Time Period,T=1f=10.8=1.25 s\text{Time Period}, T = \frac{1}{f} = \frac{1}{0.8} = 1.25 \, \text{s}

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4. Rotational Motion

In rotational motion, an object rotates around a fixed axis.

Key Concepts:

1. Angular Velocity (ω\omega): ω=ΔθΔt\omega = \frac{\Delta \theta}{\Delta t}
2. Moment of Inertia (II): Resistance to angular acceleration.
3. Torque (τ\tau): τ=Iα\tau = I\alpha, where α\alpha is angular acceleration.

Examples of CBSE Numericals:

a. Rotational Motion Example:
Question (CBSE 2020):
A wheel rotates with an angular velocity of 2 rad/s2 \, \text{rad/s} and accelerates uniformly to 10 rad/s10 \, \text{rad/s} in 4 seconds4 \, \text{seconds}. Find the angular acceleration.
Solution:
Using α=Δωt\alpha = \frac{\Delta \omega}{t}:

α=10−24=84=2 rad/s2\alpha = \frac{10 – 2}{4} = \frac{8}{4} = 2 \, \text{rad/s}^2

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5. Oscillatory Motion

Oscillatory motion is a repeated back-and-forth motion about a mean position.

Key Concepts:

1. Amplitude (AA): Maximum displacement from the mean position.
2. Time Period (TT): Time for one oscillation.
3. Frequency (ff): Number of oscillations per unit time.

Examples of CBSE Numericals:

a. Spring Oscillation Example:
Question (CBSE 2017):
A spring-mass system oscillates with a time period of 2 s2 \, \text{s}. If the spring constant is 50 N/m50 \, \text{N/m}, find the mass of the object.
Solution:
Using T=2πmkT = 2\pi\sqrt{\frac{m}{k}}:

2=2πm502 = 2\pi\sqrt{\frac{m}{50}} 1π=m50⇒1π2=m50\frac{1}{\pi} = \sqrt{\frac{m}{50}} \Rightarrow \frac{1}{\pi^2} = \frac{m}{50} m=50π2≈5.05 kgm = \frac{50}{\pi^2} \approx 5.05 \, \text{kg}

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Key Tips for Solving CBSE Numericals:

1. Identify the type of motion involved in the problem.
2. Write down all given values with proper units.
3. Choose the appropriate formula and rearrange it if necessary.
4. Solve systematically and check units.
5. Cross-check the final answer for logical consistency.

By mastering these types of motion and their applications in numericals, students can excel in understanding and solving problems in CBSE exams.

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