Calculate the moment of inertia and the rotational kinetic energy for the follow

ID: 1469376 • Letter: C

Question

Calculate the moment of inertia and the rotational kinetic energy for the following objects spinning about a central axis (in units of Joules).

a) a solid sphere with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec.

b) a thin spherical with a mass of 200 grams and a radius of 5.0cm rotating with an angular speed of 2.5rad/ sec.

c) a solid cylinder with a mass of 200grams and a radius 5.0 cm rotating with an angular speed of 2.5 rad/sec.

d) a hoop with a mass of 200 grams and a radius of 5.0cm rotating with an angular speed of 2.5 rad/sec.

Thankyou!!

(a) I = 2 M R^2 / 5

Moment of inertia = I = 2 M R^2 / 5 = 2 * 0.2 * 0.05^2 / 5 = 0.0002 kg m^2

Rotational Kinetic energy = 0.5 I w^2 = 0.5 * 0.0002 * 2.5^2 = 0.000625 J

(b) I = 2 M R^2 / 3

Moment of inertia = I = 2 M R^2 / 3 = 2 * 0.2 * 0.05^2 / 3 = 0.00033 kg m^2

Rotational Kinetic energy = 0.5 I w^2 = 0.5 * 0.00033 * 2.5^2 = 0.00103 J

(c) I = M R^2 / 2

Moment of inertia = I = M R^2 / 2 = 0.2 * 0.05^2 / 2 = 0.00025 kg m^2

Rotational Kinetic energy = 0.5 I w^2 = 0.5 * 0.00025 * 2.5^2 = 0.00078 J

(d) I = M R^2

Moment of inertia = I = M R^2 = 0.2 * 0.05^2 = 0.0005 kg m^2

Rotational Kinetic energy = 0.5 I w^2 = 0.5 * 0.0005 * 2.5^2 = 0.00156 J

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.