Semester one assignment: Find the angular speed

In summary, a thin rod of length 1.5m attached to the floor by a frictionless hinge rotates downward from rest due to an object fixed to its top. The mass of the rod is negligible compared to the object. To find the angular speed of the rod just before it hits the floor, conservation of energy can be used instead of finding the time taken for the rod to fall.
  • #1
invadertak
7
0

Homework Statement


A thin rod of lenth 1.5m is oriented vertically, with its bottom end attached to the floor by means of a frcitionless hinge. The mass of the rod may be ignored compared to the mass of and object ixed to the top of the rod. The rod, starting from rest, tips over and rotates downward. What is the angular speed of the rod just before it strikes the floor?

Homework Equations





The Attempt at a Solution


I need to find the time taken for the rod to hit the floor. I don't have enough information to use the equations of rotational kinematics without time. I can't use the equations of uniform circular motion, because the object is accelerating tangentially. I could break down the x and y motion of the object attached to the rod, but the conditions are not of free fall, surely? If I do treat the object as freefalling, it's very easy to get the time taken to hit the floor. Is that the correct way to get the time? Can I treat it as an object in free fall?
 
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  • #2
Welcome to PF!

Hi invadertak! Welcome to PF! :smile:
invadertak said:
A thin rod of lenth 1.5m is oriented vertically, with its bottom end attached to the floor by means of a frcitionless hinge. The mass of the rod may be ignored compared to the mass of and object ixed to the top of the rod. The rod, starting from rest, tips over and rotates downward. What is the angular speed of the rod just before it strikes the floor?

I need to find the time taken for the rod to hit the floor.

No … just use conservation of energy :wink:
 
  • #3
awesome!
 

1. What is angular speed?

Angular speed, also known as rotational speed or angular velocity, is a measure of how quickly an object is rotating around a fixed point. It is typically measured in radians per unit of time, such as radians per second.

2. How is angular speed different from linear speed?

Angular speed is a measure of how fast an object is rotating, while linear speed is a measure of how fast an object is moving in a straight line. Angular speed is typically measured in radians per unit of time, while linear speed is measured in distance per unit of time, such as meters per second.

3. What is the formula for calculating angular speed?

The formula for angular speed is ω = Δθ/Δt, where ω is the angular speed, Δθ is the change in angle, and Δt is the change in time. It can also be written as ω = 2πf, where f is the frequency of rotation in revolutions per unit of time.

4. How can angular speed be measured?

Angular speed can be measured using various tools such as a protractor, tachometer, or a gyroscope. These tools measure the angle of rotation and the time it takes for the rotation to occur, allowing for the calculation of angular speed.

5. What factors can affect angular speed?

The angular speed of an object can be affected by factors such as the force applied to the object, the mass and size of the object, and any external forces acting upon the object. Friction and air resistance can also impact the angular speed of an object.

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