displacement accerleration time

Question

2.2 The spindle of a washing machine rotates at 800 r/min and slows down to 300 r/min during 30 revolutions. Calculate the following: 2.2.1 The angular displacement in radians 2.2.2 The angular acceleration 2.2.3 The time required to turn through the 30 revolutions

Answer 1

2.2.1)

The spindle of a washing machine rotates at 800 r/min .

The spindle rotates at 800/60 = 13.34 revolutions per second .

 Angular frequency ω₀ = 2π ( revolutions per second )

Angular frequency ω₀ = 2π * 13.34 

Angular frequency ω₀ = 83.77 rad/sec .

The spindle slows down to 300 r/min during 30 revolutions .

The spindle rotates at 300/60 = 5 revolutions per second .

 Angular frequency ω_f = 2π ( revolutions per second )

Angular frequency ω_f = 2π * 5

Angular frequency ω_f = 31.42 rad/sec .

Angular displacement can found by using the formula (1/2)( ω₀ + ω_f )t .

Now calculate time taken for 30 revolutions :

During 30 revolutions the speed spindle 800 rpm downs to 300 rpm .

So net speed of spindle during 30 revolutions is 800 - 300 = 500 rpm .

The spindle rotates at 500/60 = 8.334 revolutions per second .

So for time required for 30 revolutions is  30/ 8.334 = 3.6 sec .

Angular displacement can found by using the formula (1/2)( ω₀ + ω_f )t .

ø = (1/2)( 83.77 +31.42  )( 3.6 )

ø = (1/2)( 115.19)( 3.6 )

ø = ( 115.19)( 1.8 )

ø = 207.342

So the angular displacement is  207.342 rad .

 

Answer 2

2.2.2)

The spindle of a washing machine rotates at 800 r/min .

The spindle rotates at 800/60 = 13.34 revolutions per second .

 Angular frequency ω₀ = 2π ( revolutions per second )

Angular frequency ω₀ = 2π * 13.34 

Angular frequency ω₀ = 83.77 rad/sec .

The spindle slows down to 300 r/min during 30 revolutions .

The spindle rotates at 300/60 = 5 revolutions per second .

 Angular frequency ω_f = 2π ( revolutions per second )

Angular frequency ω_f = 2π * 5

Angular frequency ω_f = 31.42 rad/sec .

Angular acceleration can found by using the formula α = ( ω_f - ω₀ )/t .

Now calculate time taken for 30 revolutions :

During 30 revolutions the speed spindle 800 rpm downs to 300 rpm .

So net speed of spindle during 30 revolutions is 800 - 300 = 500 rpm .

The spindle rotates at 500/60 = 8.334 revolutions per second .

So for time required for 30 revolutions is  30/ 8.334 = 3.6 sec .

Angular acceleration can found by using the formula α = ( ω_f - ω₀ )/t .

α = (31.42 - 83.77 )/3.6

α = ( -52.35 )/3.6

α = -14.542  rad/s²

So the angular acceleration is  14.542  rad/s² (clock wise) .

Answer 3

2.2.3)

The spindle of a washing machine rotates at 800 r/min .

The spindle rotates at 800/60 = 13.34 revolutions per second .

 Angular frequency ω₀ = 2π ( revolutions per second )

Angular frequency ω₀ = 2π * 13.34 

Angular frequency ω₀ = 83.77 rad/sec .

The spindle slows down to 300 r/min during 30 revolutions .

The spindle rotates at 300/60 = 5 revolutions per second .

 Angular frequency ω_f = 2π ( revolutions per second )

Angular frequency ω_f = 2π * 5

Angular frequency ω_f = 31.42 rad/sec .

Now calculate time taken for 30 revolutions :

During 30 revolutions the speed spindle 800 rpm downs to 300 rpm .

So net speed of spindle during 30 revolutions is 800 - 300 = 500 rpm .

The spindle rotates at 500/60 = 8.334 revolutions per second .

So for time required for 30 revolutions is  30/ 8.334 = 3.6 sec .

So the time taken for 30 revolution is 3.6 sec .