# Vector torque problem: Force applied to a disc

• jwbensin
In summary: Just be careful with your units and make sure they all match up.I think that would do it. Just be careful with your units and make sure they all match up.In summary, the conversation discusses the application of a force of magnitude 50N at the bottom point Q of a pinned disk with radius 8m at point P. It includes finding the angle between the force and the vector from P to Q, which is determined to be 95 degrees. It also discusses finding the magnitude of the applied torque and provides the equation |T| = 50sin(95)*8sqrt2 to calculate it.

## Homework Statement

A force of magnitude 50N is applied at the bottom point Q of a disk of radius 8m that is pinned at P
(leftmost point)

See attached picture

(a) Find the angle between the force and the vector from P to Q.
(b) Find the magnitude of the applied torque.

## Homework Equations

|T| = |F|sin(Theta)*|r|[/B]

## The Attempt at a Solution

So for part (a) I said the angle was 85 degrees but apparently that's wrong? At least according to my colleges online homework program. honestly don't know how to start part (b)

#### Attachments

• 1-4-020.png
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jwbensin said:
So for part (a) I said the angle was 85 degrees but apparently that's wrong?
Draw the vector from P to Q. Then move it so that its tail is at the same point as the tail of the force vector. Now what do you get for an angle between them?

You set a usual OXYZ reference system, with origin at point P, and note that the coordinates of point Q are: Q(0,8,-8), and the vector position corresponding to point Q, remains:
r = PQ = <8,-8,0>
Then, note that the components of the force applied at point Q are:
F = <50sin(40º), -50cos(40º), 0>.
Then, to calculate the torque with respect to an axis parallel to the OX axis passing through point P, you have to solve the vector product:
T = r x F.

tnich said:
Draw the vector from P to Q. Then move it so that its tail is at the same point as the tail of the force vector. Now what do you get for an angle between them?
95 Degrees?

jwbensin said:
95 Degrees?
Yes. Now you have everything you need to substitute into your equation for |T|.

tnich said:
Yes. Now you have everything you need to substitute into your equation for |T|.
So would I just simply do |T| = 50sin(95)*8sqrt2 or am I missing something?

tnich
jwbensin said:
So would I just simply do |T| = 50sin(95)*8sqrt2 or am I missing something?
I think that would do it.

## What is a vector torque problem?

A vector torque problem is a physics problem that involves calculating the rotational force, or torque, applied to a disc. This requires understanding the principles of vectors, which are quantities that have both magnitude and direction.

## How is force applied to a disc?

Force is applied to a disc by exerting a push or pull on the disc in a specific direction. This force creates a torque, which causes the disc to rotate around a fixed axis.

## What factors affect the vector torque of a disc?

The magnitude and direction of the force applied, as well as the distance between the force and the axis of rotation, all affect the vector torque of a disc. The angle between the force and the lever arm also plays a role in determining the torque.

## How is vector torque calculated?

Vector torque is calculated by multiplying the force applied by the distance between the force and the axis of rotation, and then multiplying that by the sine of the angle between the force and the lever arm.

## Why is understanding vector torque important?

Understanding vector torque is important in many fields, including engineering, mechanics, and physics. It allows scientists and engineers to design and analyze systems that involve rotational motion, such as gears and motors.