A 220g block on a 54.0cm -long string swings in a circle on a horizontal, frictionless table at 70.0 rpm.

A) What is the speed of the block? m/s
B) What is the tension in the string? N

speed= angularvelociy*radius=2PI*70/60*.54

tension= massinKg*V^2/r

To find the speed of the block, we can convert the given angular velocity in revolutions per minute (rpm) to radians per second (rad/s). Then we can use the formula for the speed of an object moving in a circular path.

A) To convert rpm to rad/s, we multiply the angular velocity by 2π/60, since there are 2π radians in one revolution and 60 seconds in one minute.

Given:
Angular velocity (ω) = 70.0 rpm
Radius of the circular path (r) = 54.0 cm

First, let's convert the angular velocity to rad/s:
ω = 70.0 rpm * (2π/60)
= 7.33 rad/s

The speed of the block moving in a circular path is equal to the product of the angular velocity and the radius of the circular path.
Speed (v) = ω * r

Let's convert the radius from centimeters to meters:
r = 54.0 cm * (1 m/100 cm)
= 0.54 m

Now, we can calculate the speed of the block:
v = 7.33 rad/s * 0.54 m
= 3.96 m/s

Therefore, the speed of the block is 3.96 m/s.

B) To find the tension in the string, we need to consider the forces acting on the block in the circular motion. The tension force in the string provides the centripetal force required to keep the block moving in a circular path.

The centripetal force can be calculated using the formula:
F = m * (v^2 / r)

Given:
Mass of the block (m) = 220 g = 0.220 kg
Speed of the block (v) = 3.96 m/s
Radius of the circular path (r) = 0.54 m

Now, let's calculate the tension in the string:
F = 0.220 kg * (3.96 m/s)^2 / 0.54 m
≈ 3.21 N

Therefore, the tension in the string is approximately 3.21 N.