The angular speed of a whecl is increased from 1200 rpm to 3120 rpm. in 16 sccond. (rpm means re

The angular speed of a whecl is increased from 1200 rpm to...

Key Concepts

Uniform Angular Acceleration

Uniform angular acceleration refers to a constant rate of change of angular velocity over time, analogous to constant linear acceleration in translational motion. It is calculated by taking the difference between the final and initial angular velocities and dividing by the time interval during which this change occurs.

Angular Kinematics Equations

Angular kinematics deals with the motion of rotating systems under uniform (or non-uniform) angular acceleration. The fundamental equations include relations like ? = ?? + ?t for angular velocity and ? = ??t + ½?t² for angular displacement, which parallel the kinematic equations used in linear motion.

Conversion of Angular Speed Units

This concept involves converting angular speeds given in revolutions per minute (rpm) to radians per second (rad/s), which are the standard SI units for angular velocity. The conversion uses the facts that one revolution is equal to 2? radians and one minute is equal to 60 seconds.

Conversion Between Radians and Revolutions

This concept involves converting angular displacement measured in radians to revolutions, or vice versa. Since one full revolution corresponds to 2? radians, this conversion is essential for interpreting angular motion in practical contexts where the number of complete turns is required.

Transcript

00:01 Hello everyone we are going to understand this question here given in the question given angular speed of wheel initial angular speed of wheel that is represented by omega not which is equal to 2 pi into f here f is the initial frequency initial frequency given in the question that is 1200 r p m so initial angular speed omega not is equal to 2 pi into 1200 here it is given in rpm now converting this into second so we will get 200 rotation per second one minute is equal to 60 second so we can write 1 upon 60 radian per second now doing further calculation we will get we will get 40 pi into 40 into pi radian per second, radian per second.

01:19 And final angular speed, omega f is equal to 2 pi into final angular frequency and here it is given in the question that final angular frequency is 3 ,120 rpm.

01:47 Now converting into second so so we will get 31 20 into 1 .60 rps radian per second, rotation per second or revolution per second.

02:04 So after doing further calculation we will get final angular speed that is represented by omega f.

02:13 So 2 pi into 3 ,120.

02:17 20 upon 60 radian per second.

02:24 Now doing further calculation we will get omega f is equal to 105 radian per second.

02:46 This is the final angular speed.

02:48 So in the part a we have to calculate the angular acceleration and here time is given, time taken to increase this speed that is given 16 seconds.

02:59 Let angular acceleration be alpha.

03:06 Let angular representation let angular acceleration be alpha.

03:21 So we can write omega f is equal to omega -0 plus alpha into t.

03:33 Here final angular speed is given 104 pi and initial angular speed is given for t pi plus alpha into value of t that is 16 so doing further calculation we will get 104 pi minus 40 pi upon 16 radian per second square now doing further calculation we will get alpha is equal to alpha is equal to 104 minus 40 that will give 64 pi upon 16 radian per second square.

04:28 Now doing further calculation we will get alpha is equal to 4 pi radian per second square...

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