Equations for Projectile Motion

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Equations for Projectile Motion
Horizontal Vertical ax0
ay - g vx constant
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Steps in Solving Problems

1. Draw free-body diagram for every object that is
   free
2. Select coordinate system such that one of the
   axis is along the direction of acceleration
3. Write out the equations of motion for the x and y
   coordinate

1. Step 2 should guarantee that the sum of the
   forces in at all but one direction equals zero.
2. Solve the equations simultaneously

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Non-Conservative Forces

• If work is done by non-conservative forces

• The sign of WNC is very important
• A motor adds energy so WNC is positive and E2 gt
  E1
• Friction dissipates energy so WNC is negative and
  E2 lt E1

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Example 6-5 (43) The roller-coaster car shown is
dragged up to point 1 where it is released from
rest. Assuming no friction, calculate the speed
at points 2, 3, and 4. Let point be the height
where P.E. 0
Ch 6
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Continued
Example 6-5 (43) The roller-coaster car shown is
dragged up to point 1 where it is released from
rest. Assuming no friction, calculate the speed
at points 2, 3, and 4. Let point be the height
where P.E. 0
Ch 6
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Conservation of Momentum
In the collision of two isolated objects, the
only forces are between the two objectsthese are
called internal forces. In this case
initial momentum final momentum
The total momentum of an isolated system of
bodies remains constant.
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Radial and Tangential Acceleration
A point on a rotating wheel always has
centripetal acceleration and it will have
tangential acceleration if the wheel has angular
acceleration.
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Kinematic Equations for Uniformly Accelerated
Motion
The angular equations for constant angular
acceleration are derived the same as for constant
linear acceleration.
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Rotational Dynamics
Torque is necessary for angular acceleration
This is expressed as
where I is called the moment of inertia
Compare this with Newtons Second Law

• t is the equivalent of force for rotational
  motion
• I is the equivalent of mass for rotational motion

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Example 8-5
A 1.5 kg mass is
attached to a cord wrapped around a heavy pulley
of mass 4.00 kg and radius 33.0 cm. The pulley
is a solid cylinder. Calculate the acceleration
of the mass.