Circular Motion

Physics Tutorial

Circular Motion

Intro

Circular Motion deals with the forces exerted on and by an object travelling in a circle. To understand this topic, it is crucial to know several things:
(1) Newton’s Second Law: F=ma where F is the variable for Force in Newtons (N), m is the variable for mass in kilograms (kg), and a is the variable for acceleration in meters per second squared (m/(s^2))
(2) That all acceleration is exerted towards the center of the circle and not outward. (3) Acceleration can be found by the equation velocity squared divided by the radius ((v^2)/r)

Sample Problem

A horizontal force of 300 N is exerted on a 2.5 kg discus as it is rotated uniformly in a circle (at arms length) of radius 1.5 m. Calculate the speed of the discus

Solution

1. Starting with the equation F=ma, we can plug in the numbers given by the question.
2. 300 N is the force, 2.5 kg is the mass so we need the acceleration, so: 300=2.5a.
3. To isolate the variable we divide each side by 2.5: (300/2.5)=(2.5a/2.5) = 120a.
4. Now we know that the acceleration equals 120 m/(s^2), but we still need to find the velocity.
5. a = (v^2)/r is the equation used to derive velocity from acceleration. We know that a = 120 m/(s^2) and r = 1.5 m. Now we can plug in: 120 = (v^2)/1.5.
6. Multiply each side side by 1.5 for 180 = v^2.
7. Now to isolate v find the square root of each side: 13.4164 = v
8. Rounding to the appropriate number of significant figures, we find that v = 13, so our answer is 13 m/s



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