Math Problem Statement

A torque of 44 N·m producing a counter clockwise rotation is applied to a wheel about its axle. A frictional torque of 16 N · m acts at the axle. What is the net torque about the axle of the wheel

Solution

The net torque (τnet\tau_{\text{net}}) acting on the wheel can be found by considering the applied torque and the opposing frictional torque.

Given:

  • Applied torque (τapplied\tau_{\text{applied}}) = 44 N·m (counterclockwise)
  • Frictional torque (τfriction\tau_{\text{friction}}) = 16 N·m (clockwise)

Since counterclockwise torque is considered positive and clockwise torque negative, the net torque will be:

τnet=τappliedτfriction\tau_{\text{net}} = \tau_{\text{applied}} - \tau_{\text{friction}} τnet=44N\cdotpm16N\cdotpm=28N\cdotpm\tau_{\text{net}} = 44 \, \text{N·m} - 16 \, \text{N·m} = 28 \, \text{N·m}

So, the net torque is 28N\cdotpm28 \, \text{N·m} in the counterclockwise direction.

Would you like more details or clarification on this?

Here are some related questions:

  1. How do you calculate torque?
  2. What is the relationship between torque and rotational acceleration?
  3. How do you determine the direction of torque?
  4. What factors affect the amount of frictional torque in a system?
  5. How does net torque influence angular velocity?

Tip: Torque is the rotational equivalent of force, so always consider both magnitude and direction when calculating net torque!

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Math Problem Analysis

Mathematical Concepts

Torque
Rotational Dynamics

Formulas

\( \tau_{\text{net}} = \tau_{\text{applied}} - \tau_{\text{friction}} \)

Theorems

Net torque theorem

Suitable Grade Level

Grades 9-12