Math Problem Statement

An object's moment of inertia is 1.70 kgm2 . Its angular velocity is increasing at the rate of 3.10 rad/s2 . What is the net torque on the object?

Solution

The net torque on an object can be found using Newton's Second Law for Rotation, which states:

τ=Iα\tau = I \alpha

Where:

  • τ\tau is the net torque,
  • II is the moment of inertia,
  • α\alpha is the angular acceleration.

From the problem, we are given:

  • Moment of inertia, I=1.70kgm2I = 1.70 \, \text{kg} \cdot \text{m}^2,
  • Angular acceleration, α=3.10rad/s2\alpha = 3.10 \, \text{rad/s}^2.

Substitute these values into the equation:

τ=1.70kgm2×3.10rad/s2\tau = 1.70 \, \text{kg} \cdot \text{m}^2 \times 3.10 \, \text{rad/s}^2

τ=5.27Nm\tau = 5.27 \, \text{N} \cdot \text{m}

So, the net torque on the object is 5.27Nm5.27 \, \text{N} \cdot \text{m}.

Would you like more details or clarifications on this?

Here are some related questions:

  1. How does the moment of inertia depend on the shape of an object?
  2. What is the relationship between torque and angular momentum?
  3. How can you calculate angular acceleration from torque and moment of inertia?
  4. How does the rotational equivalent of Newton's second law apply to a rotating disk or cylinder?
  5. What are the units of torque, and how do they relate to force and distance?

Tip: When calculating torque, always ensure that the moment of inertia and angular acceleration are in consistent units.

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Math Problem Analysis

Mathematical Concepts

Rotational Motion
Moment of Inertia
Angular Acceleration
Torque

Formulas

\tau = I \alpha

Theorems

Newton's Second Law for Rotation

Suitable Grade Level

Grades 9-12