Question

1.What is the magnitude of angular momentum of a 1070 kg car going around a circular curve with a 15.0 m radius at 12.0 m/s? Assume the origin is at the center of the curve's arc.

2.A solid uniform sphere of mass 3.7 kg and radius 0.051 m rotates with angular velocity 7.3 rad/s about an axis through its center. Find the sphere’s rotational kinetic energy.

3.How far from the pivot of a horizontal seesaw should a 28.0-kg child sit in order to produce a torque of 310 N·m?

Answer 1

here,

1)

the mass of car , m = 1070 kg

radius of curve , r = 15 m

speed , v = 12 m/s

the agnitude of angular momentum , L = m * v * r

L = 1070 * 15 * 12 kg.m^2 /s

L = 1.93 * 10^5 kg.m^2 /s

2)

the mass of sphere , m = 3.7 kg

radius , r = 0.051 m

angular speed , w = 7.3 rad/s

the sphere's rotational kinetic energy , KEr = 0.5 * I * w^2

KEr = 0.5 * ( 0.4 * m * r^2) * w^2

KEr = 0.2 * 3.7 * 0.051^2 * 7.3^2 J

KEr = 0.103 J

3)

mass of child , m = 28 kg

let the distance from the pivot be r

the torque , T = m * g * r

310 = 28 * 9.81 * r

solving for r

r = 1.13 m

the distance from the pivotis 1.13 m