One revolution is 2 π radians. Let’s use the following equation to solve this problem.

ωf^2 = ωi^2 + 2 * α * θ, ωi = 0

ωf^2 = 2 * 4 * 2 * π

ω = 4 * √π

To one significant digit, this is approximately 7 rad/s.

From equations of motion

w^2 - w0^2 = 2*alpha*theta

theta = 2pi

W^2 = 2*4*2pi ==>w = sqrt(16pi) = 4 sqrt(pi) rad/s = 7.089 rad/s

You can use all your known linear formulae on circular motion.

v^2 = 2as

v = sqrt( 2as) = sqrt( 2 * 4 * 2 * pi() ) ( the "distance" moved is 2 pi() radians )

= 7.09 radians per second.

Why learn a whole heap of "new" formulae if you already know them all anyway.

You have :

-----------------------

a = dw/dt --------> dt = dw/a

w = d rad / dt ----> dt = d rad / w

dt = dt = dw/a = d rad / w

w dw = a d rad/dt

Integral [ w dw ] w1--->w2 = Integral [ a drad ] rad1--->rad2

( w2^2 - w1^2 ) / ( 2 ) = ( a ) ( rad2 - rad1 )

w2 = SQRT [ ( 2 ) ( a ) ( 2 pi rad ) ] = SQRT [ (4 ) ( pi ) ( a ) ]

w2 = SQRT [( 2) ( 2 pi rad/rev ) ( 4 rad/s^2 )]

w2 = SQRT [ ( 16 ) ( pi rad^2/s^2 ) ]

w2 = 7.1 rad/s <--------------------------------------

For linear acceleration we have vf² = vi² + 2as.

The equivalent for rotational acceleration is ωf² = ωi² + 2αθ

Since one rotation is an angular displacement of θ = 2π:

ωf² = 0² + 2*4*2π

. . . = 50.27

ωf = 7.09 rad/s

2pi = 1/2 * a * time^2

find the time

angular speed = angular acceleration * time

7,1 rad/sec

- Can we make electricity with heat?
- Atheists, do you believe this?
- Can someone simply describe the einstein s general theory of relativity?
- What keeps the air pressure on Earth?
- Is loudspeaker a motor or a generator?

- Arts & Humanities
- Beauty & Style
- Business & Finance
- Cars & Transportation
- Computers & Internet
- Consumer Electronics
- Dining Out
- Education & Reference
- Entertainment & Music
- Environment
- Family & Relationships
- Food & Drink
- Games & Recreation
- Health
- Home & Garden
- Local Businesses
- News & Events
- Pets
- Politics & Government
- Pregnancy & Parenting
- Science & Mathematics
- Social Science
- Society & Culture
- Sports
- Travel