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:
Where:
- is the net torque,
- is the moment of inertia,
- is the angular acceleration.
From the problem, we are given:
- Moment of inertia, ,
- Angular acceleration, .
Substitute these values into the equation:
So, the net torque on the object is .
Would you like more details or clarifications on this?
Here are some related questions:
- How does the moment of inertia depend on the shape of an object?
- What is the relationship between torque and angular momentum?
- How can you calculate angular acceleration from torque and moment of inertia?
- How does the rotational equivalent of Newton's second law apply to a rotating disk or cylinder?
- 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
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