PHYS 1P21 Lecture Notes - Lecture 6: Horse Length, Abscissa And Ordinate, Tennis Ball

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19 May 2016

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Kinematics equations in two dimensions (for constant acceleration) If an object has non-zero acceleration, then it experiences a change in velocity. On the other hand, if the acceleration of an object is zero, then there is no change in velocity, which means the velocity is constant if acceleration is zero The key fact of chapter 3, which is supported by innumerable observations and precision experiments, is this: For an object moving in two (or three) dimensions, we can separate the kinematical vector quantities into components. Thus, we can analyze a two-dimensional (or three-dimensional) motion by separating it into components. This strategy fits in with the general strategy of reductionism, which is used frequently in mathematics and science. There are many other examples of reductionism, and you"ll discover many if you look for them. Here are the kinematics equations for two-dimensional motion, as written in the textbook (see page 59 in section 3. 2):

Related Questions

to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve the motion of a particle with constant, nonzero angular acceleration. The kinematic equations for such motion can be written as

$\theta (t) = \theta_0 +\omega_0t + \frac{1}{2}\alpha t^2$

and

$\omega (t) = \omega_0 + \alpha t$ .

Here, the symbols are defined as follows:

is the angular position of the particle at a time t.
is the initial angular position of the particle.
is the angular velocity of the particle at a time t.
is the initial angular velocity of the particle.
is the angular acceleration of the particle.
is the time that has elapsed since the particle was located at its initial position.

In answering the following questions, assume that the angular acceleration is constant and nonzero: $\alpha \neq 0$ .

True or false: The quantity represented by theta

is a function of time (i.e., is not constant).

	true
	false

True or false: The quantity represented by theta_0

is a function of time (i.e., is not constant).

	true
	false

True or false: The quantity represented by omega_0

is a function of time (i.e., is not constant).

	true
	false

True or false: The quantity represented by omega

is a function of time (i.e., is not constant).

	true
	false

Which of the following equations is not an explicit function of time

? Keep in mind that an equation that is an explicit function of time involves

as a variable.

	$\theta=\theta_0+\omega_0 t+\frac{1}{2}\alpha t^2$
	$\omega=\omega_0+\alpha t$
	$\omega^2=\omega_0^2+2\alpha(\theta-\theta_0)$

In the equation $\omega=\omega_0+\alpha t$ , what does the time variable

represent?

Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true.

	the moment in time at which the angular velocity equals $\omega_0$
	the moment in time at which the angular velocity equals $\omega$
	the time elapsed from when the angular velocity equals $\omega_0$ until the angular velocity equals $\omega$

Consider two particles A and B. The angular position of particle A, with constant angular acceleration, depends on time according to $\theta_{\rm A}(t)=\theta_0+\omega_0t+\frac{_1}{^2}\alpha t^2$ . At time $t=t_1$ , particle B, which also undergoes constant angular acceleration, has twice the angular acceleration, half the angular velocity, and the same angular position that particle A had at time $t=0$ .

Which of the following equations describes the angular position of particle B?

	$\theta_{\rm B}(t)=\theta_0+2\omega_0t+\frac{1}{4}\alpha t^2$
	$\theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0t+\alpha t^2$
	$\theta_{\rm B}(t)=\theta_0+2\omega_0(t-t_1) +\frac{1}{4}\alpha (t-t_1)^2$
	$\theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0(t-t_1)+\alpha (t-t_1)^2$
	$\theta_{\rm B}(t)=\theta_0+2\omega_0(t+t_1) +\frac{1}{4}\alpha (t+t_1)^2$
	$\theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0(t+t_1)+\alpha (t+t_1)^2$

How long after the time t_1

does the angular velocity of particle B equal that of particle A?

	$\frac{\omega_0}{4\alpha}$
	$\frac{\omega_0+4\alpha t_1}{2\alpha}$
	$\frac{\omega_0+2\alpha t_1}{2\alpha}$
	The two particles never have the same angular velocity.

tealwildebeest936

Part A

An object cannot remain at rest unless which of the following holds?

The net force acting on it is zero.

The net force acting on it is constant and nonzero.

There are no forces at all acting on it.

There is only one force acting on it.

Part B

If a block is moving to the left at a constant velocity, what can conclude?

There is exactly one force applied to the block.

The net force applied to the block is directed to the left.

The net force applied to the block is zero.

There must be no forces at all applied to the block.

Part C

A block of mass 2kg is acted upon by two forces: 3N (directed to the left) and 4N (directed to the right). What can you say about the block's motion?

It must be moving to the left.

It must be moving to the right.

It must be at rest.

It could be moving to the left, moving to the right, or be instantaneously at rest.

Part D

A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________.

continuously changing direction

moving at a constant velocity

moving with a constant nonzero acceleration

moving with continuously increasing acceleration

amethystraven1

The figure shows three graphs, A, B, C, which collectively describe the motion of an object in one dimension. The horizontal axis of each graph is time (symbol t). The vertical axes of the graphs are different. For one graph the vertical axis is position (symbol x), for another, it is the velocity (symbol v), and for another, it is acceleration (symbol a). Where the axes across is the point of zero for both time and the quantity corresponding to the vertical axis. Part A: For which sequence of graphs is the vertical coordinate position, velocity, and acceleration, respectively? (e.g., If you think graph Y is position versus time, graph X is velocity versus time, and graph Z is acceleration versus time, then your answer is Y, X, Z.). Multiple choice: 1)C, A, B 2)A, C, B 3)C, B, A 4)B, C, A 5)B, A, C 6)A, B, C. Part (b) Which one of the following situations can be most accurately represented by the graph, consistent with your answer to part (a)? (1) A car driving in the negative x-direction suddenly shifts into reverse and, with tires spinning, slows to a momentary stop before beginning to move in the position x-direction. (2)A car driving in the position x-direction slams on its brakes and comes to rest. (3) A rock is dropped from the rest from the top of a tall building. Assume air drag can be neglected, in which case its speed increases by the same amount each second. Take upward to be the position x-direction. (4) A sprinter runs a 100-meter dash and she runs in the negative x-direction. Starting from rest, she has a constant acceleration for the first 50 meters, then a constant speed for the remaining 50. Multiple choices: 1)4, 2)3, 3)2, 4)1.

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PHYS 1P21 Lecture Notes - Lecture 6: Horse Length, Abscissa And Ordinate, Tennis Ball

PHYS 1P21 Full Course Notes

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