Physics help?

Question

1. A girl sits on a merry go round 1.5 m from the center. If the girl moves through an arc length of 2.5 m, through what angular displacement did she move?

2. A passenger care on a Ferris wheel moves through a distance of 12m before it stops to drop off passengers. If the passenger carts are all 35 m from the axis of rotation of the Ferris wheel, what angular displacement does each cart mover through during this part of the ride?

3. A girl ties a toy airplane to the end of a 1.8 m string and swings it around her head. What is the angular speed if the plane movers through an arc length of 6.3 during 1.5s. If the plane has a mass of .75 kg, what is the centripetal acceleration and what is tension on the string?

Answer 1

(1)

Distance from Centre = 1.5m.

Arc Length = 2.5m

Angular Displacement = Arc Length / Radius.

Angular Displacement = 2.5 / 1.5

Angular Displacement = 1.667 radians.

Therefore Angular Displacement  = 1.667 radians.

Answer 2

(2)

Distance from axis of rotation = 35 m.

Distance moved by Ferris Wheel to drop Passengers = 12 m.

Angular Displacement = Arc Length / Radius.

Angular Displacement = 12 / 35

Angular Displacement = 0.3428 radians.

Therefore Angular Displacement  = 0.3428 radians.

Answer 3

(3)

Distance from the toy = 1.8 m.

Arc Length = 6.3 m during 1.5sec.

Mass of the Plane = 0.75 kg

Angular Displacement = Arc Length / Radius.

Angular Displacement = 6.3 / 1.8

Angular Displacement = 3.5 radians.

Angular Displacemnt for 1.5 sec = 3.5 / 1.5

Angular Velocity = 2.33 radians /sec.

Velocity = Angular Velocity * radius.

Velocity = 2.33 * 1.8

Velocity v = 4.2 m/sec.

Centripetal Accelation = (v² / r) = (4.2)² / 1.8 =  9.8 m/sec².

Tension in the string = mg

Tension in the string = 0.75 * 9.8 = 7.35 N.

Therefore

Angular Displacement = 3.5 radians.

Centripetal Accelation =  9.8 m/sec².

Tension in the string = 7.35 N.