Download presentation

Presentation is loading. Please wait.

Published byOlivia Castillo Modified over 4 years ago

1
Circular Motion

2
Imagine a hammer (athletics variety) being spun in a horizontal circle At a constant speed

3
Birds-Eye View v ω r

4
v = rω

5
Side View T mg ω

6
We know that the hammer is accelerating….. Because the hammer is constantly changing direction (although the speed is constant)

7
So from Newtons First and Second Laws, there must be a resultant force Equal to mass x acceleration

8
For circular motion….. Acceleration = v 2 r or rω 2 (using v = rω )

9
So the resultant force ….. = mv 2 r or mrω 2 (using v = rω )

10
Which direction do the resultant force and acceleration act in? Towards the centre of the described circle

11
So if we look at our original diagram…….

12
If the circle has a radius,r…. T mg ω

13
We can find the resultant force by resolving in the plane of the circle. The only force acting in the horizontal plane is the tension So by resolving T = mrω 2

14
Very important point! The circular force is not an additional force – it is the resultant of the forces present.

15
Typical exam style question Ball hangs from a light piece of inextensible string and describes a horizontal circle of radius,r and makes an angle θ with the vertical. If the mass of the ball is m kg i)calculate the tension, T in the string ii)calculate the angular velocity, ω in terms of g, r and θ.

16
Diagram r θ mg T

17
To find the tension…. Resolve vertically Ball is not moving up or down so vertical components must be equal Tcosθ = mg so T = mg cosθ

18
To find the angular velocity, ω… Resolve horizontally Circular motion so we know that there is a resultant force towards the centre Tsinθ = mrω 2 ω = Tsinθ mr

19
But…… T = mg cosθ so ω = Tsinθ mr Becomes ω = gtanθ r

20
Easy?

Similar presentations

OK

Aim: How can we apply Newton’s 2 nd Law of Acceleration? Do Now: An object with mass m is moving with an initial velocity v o and speeds up to a final.

Aim: How can we apply Newton’s 2 nd Law of Acceleration? Do Now: An object with mass m is moving with an initial velocity v o and speeds up to a final.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on project tiger for class 10 Ppt on land soil water natural vegetation and wildlife resources Ppt on intelligent manufacturing in industrial automation Ppt on power diode testing Ppt on the art of war Ppt on dth service free download Ppt on software quality in software project management Free ppt on rainwater harvesting Ppt on next generation 2-stroke engine Ppt on ready to eat food