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3-Projectile Motion and Ucm

Projectile motion involves two independent motions: horizontal motion with constant velocity and vertical motion with constant acceleration due to gravity. Uniform circular motion describes an object moving at a constant speed in a circular path, experiencing centripetal acceleration towards the center and requiring a centripetal force to maintain the circular motion. Key equations relate the tangential speed, radius, period of revolution, frequency, centripetal acceleration, and centripetal force for uniform circular motion.

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Laarni Faye Sarmiento
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189 views2 pages

3-Projectile Motion and Ucm

Projectile motion involves two independent motions: horizontal motion with constant velocity and vertical motion with constant acceleration due to gravity. Uniform circular motion describes an object moving at a constant speed in a circular path, experiencing centripetal acceleration towards the center and requiring a centripetal force to maintain the circular motion. Key equations relate the tangential speed, radius, period of revolution, frequency, centripetal acceleration, and centripetal force for uniform circular motion.

Uploaded by

Laarni Faye Sarmiento
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MODULE 3: PROJECTILE MOTION AND UNIFORM CIRCULAR MOTION

INTRODUCTION:
A projectile is an object moving in 2 dimensions under the influence of gravity. For example, a ball moving
through the air is a projectile. We will ignore the effects of air resistance on the projectile. In general, any two-
dimensional motion is made up of two, independent, simultaneous one-dimensional motions at right angles to
each other. These are called components of the motion.
The horizontal component of the motion of a projectile is motion with constant velocity. The vertical
component of the motion of a projectile is motion with constant acceleration.

Projectile Motion

- is a combination of horizontal motion with constant velocity and vertical motion with constant acceleration.

1st Condition/Projectile A(downward motion)


V1x
Ɵ Horizontal Motion:(a=o)
V1 *Velocity
V1y = 0 V1x= V1 cos θ = V2x
*Displacement
R= V1x(t)= V1 cos θ (t)
Vertical Motion:(a=g=9,8 m/s2)
*Velocity
V1y=0 V2y2=2gH
V2y=gt
*Displacement
H=1/2gt2 H=V2y2/2g
Combination:
R= V1cos θ ( 2H/g)1/2

V2x
Ɵ

V2
V2y

2nd Condition/Projectile B(upward and downward motion) Horizontal Motion:(a=g=9.8 m/s2)


*Velocity
V2= 0 V1x= V1 cos θ = V2x
*Displacement
R= V1x(T)= V12 sin2θ/g
Rmax= V12/g
Vertical Motion:(a=g=9,8 m/s2)
*Velocity
Hmax V1y= V1 sinθ V2y= V1 sinθ-gt
V1y V2y2= (V1 sinθ)2 - 2gh
V1 *Displacement
H=V1 sinθ(t) - 1/2gt2 Hmax= (V1sinθ)2/2g
Ɵ Time
V2x
V1x R and Rmax Ɵ *Time rise/Time fall *Time of flight
t=V1sinθ/g T= 2V1sinθ/g
V2y V2
Uniform Circular Motion

- is a motion of an object travelling at constant/uniform speed on a circular path.


An example of this is an object tied and whirled above your head:

V V * The speed of the object is the magnitude of the


velocity. The speed is constant.
*Time element and frequency:
Period(T) – is the time required to travel once
around the circle – that is to make one
complete revolution.
Frequency(f) – refer the number of cycle per unit
of time.
ac T = 1/f ; f = 1/T
*Since, v = d/t and d is equal to circumference of a
Fc circle(C) therefore,
v = 2πr/T (tangential speed)
*Centripetal accleration – is the acceleration of an
object that points toward the center of a circle.
ac = v2/r
*Centripetal force – is an inward force that provides
V V an object to move in circular path with its centripetal
acceleration.
Fc = mv2/r

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