Question

a torque of 400 Nm acting on a body of mass 40 kg produces an angular acceleration of 20 rad/s². Calculate the moment of inertia and radius of gyration of the body.

Answer 1

Answer:

Moment of Inertia = 20 Kg m^2

Radius of Gyration = 0.707 m

Explanation:

Given,

The torque = 400 Nm

The mass of the body = 40 kg

Angular acceleration = 20 rad/ s^2

Moment of Inertia = Torque/ Angular acceleration

Moment of Inertia = 400/ 20

Moment of Inertia = 20 Kg m^2

moment of Inertia = Mass(Radius of gyration)^2

20 = 40 K^2

K^2 = 1/2

K = Under root (1/2)

K = 0.707 m

Radius of gyration = 0.707 m

Answer 2

Answer:

Moment of Inertia = 20 Kg m^2

Radius of Gyration = 0.707 m

Explanation:

Given,

The torque = 400 Nm

The mass of the body = 40 kg

Angular acceleration = 20 rad/ s^2

Moment of Inertia = Torque/ Angular acceleration

Moment of Inertia = 400/ 20

Moment of Inertia = 20 Kg m^2

moment of Inertia = Mass(Radius of gyration)^2

20 = 40 K^2

K^2 = 1/2

K = Under root (1/2)

K = 0.707 m

Radius of gyration = 0.707 m