Physics help ASAP?

Question

A 7.0 m diameter merry-go-round is initially turning with a 4.6 s period. What is the speed of a child on the rim? 

A 170 g block on a 50 cm-long string swings in a circle on a horizontal, frictionless table at 80 rpm. 
(a) What is the speed of the block? 
(b) What is the tension in the string?

Answer 1

The diameter of the Merry-go-round = 7.0 m

Radius of the Merry-go-round = 3.5 m.

Time = 4.6 sec.

Speed = Distance / time

Distance travelled by the Merry-go-round = 2πr = 2*π*3.5 = 21.99 m.

Speed = 21.99 / 4.6

Speed = 4.78 m/sec

Therefore the speed of the child on the rim is 4.78 m/sec.

Answer 2

2(a)

The mass of the block = 170 g.

String length = 50cm = 0.5 m.

Angular speed = 80 rpm

Angular speed = (80*2π) /60 rad/sec = 8.377 rad/sec

We know that Angular Speed = Tangential Velocity * radius

ω = v*r

v = ω / r

v = 8.377 rad/sec / 0.5

v = 16.755 m/sec

Therefore speed of the block  is 16.755 m/sec.

Answer 3

2(b)

The mass of the block = 170 g = 0.17.

String length = 50cm = 0.5 m.

Angular speed = 80 rpm

Angular speed = (80*2π) /60 rad/sec = 8.377 rad/sec

We know that Angular Speed = Tangential Velocity * radius

ω = v*r

v = ω / r

v = 8.377 rad/sec / 0.5

v = 16.755 m/sec

Therefore Velocity = 16.755 m/sec

Tension in the string = mv²/r

T = (0.17*(16.755)²) / 0.5

T = 95.45 N

Therefore theTension in the string is 95.45 N.