Question

A 200g block on a 50cm long string swings in a circle, it's frictionless and 75rpm. What is its speed and tension on string

Answer 1

The speed of the block is given by:

$V = w * R$

Where,

w: angular speed

r: radius of the circular path.

The angular velocity must be in radians over seconds:

$w = (75) * (2\pi) * (\frac{1}{60})\\w = 7.85$

The radius must be in the subway:

$R = (50) * (\frac{1}{100})\\R = 0.5 m$

Then, the speed is given by:

$V = (7.85) * (0.5)$

$V = 3.925 \frac{m}{s}$

The tension of the rope is the centripetal force.

By definition, the centripetal force is:

$F = m * (\frac{V^2}{R})$

Where,

m: mass of the block in kilograms

Substituting values:

$F = 0.2 * (\frac{3.925 ^ 2}{0.5})\\F = 6.2 N$

Answer:

its speed and tension on string are:

$V = 3.925 \frac{m}{s}\\ F = 6.2 N$

Answer 2

Angular velocity = (75x2pie)/60
                          =2.5pie ras^-1 
linear velocity(or speed) at end of string, v = radius x angular velocity
                                                           v= 0.5 x 2.5pie
                                                           v=3.93 ms^-1

tension of string (I beleve is centeral force aplied by string), F= (mv^2)/r
                                                                                      F= (0.2 x 3.93^2)/0.5
                                                                                      F=6.18 N
(sorry if wrong)