NAME: BISMONTE, MA. ELIZABETH HOMEWORK # 2 
SUBJECT/SECTION: PHY11/B6 SCORE: 
TOPIC: RIGID BODIES, ROTATIONAL KINEMATICS, MOMENT OF INERTIA
1. A child is pushing a merrygoround. The angle through the merrygoround has turned varies with time according to θ(t) = γt + βt3, where γ = 0.400 rad/s and β = 0.0120 rad/s3. a. Calculate the angular acceleration as a function of time.
b. What is the initial value of the angular velocity?
c. Calculate the instantaneous value of the angular velocity at t =5.00 s and the average angular velocity for the time interval t = 0 to t = 5.00 s.
2. At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by to θ(t) = (250 rad/s)t  (20.0 rad/s2)t2 – (1.50 rad/s3)t3. a. At what time is the angular velocity of the motor shaft zero?
b. Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity.
c. How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero?
d. How fast was the motor shaft rotating at t =0, when the current was reversed?
e. Calculate the average angular velocity for the time period from t = 0 to the time calculated in part a.
3. A wheel is rotating about an axis that is in the z direction. The angular velocity is – 6.00 rad/s at t = 0, increases linearly with time, and is +8.00 m/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. a. Is the angular acceleration during this time interval positive or negative?
b. During what time interval is the speed of the wheel increasing? Decreasing?
c. What is the angular displacement of the wheel at t = 7.00s?
4. A turntable rotates with a constant 2.25 rad/s2 angular acceleration. After 4.00 s it has rotated through an angle of 60.0 rad. What was the angular velocity of the wheel at the...
...pivot point. L2 > L1. Calculate all torques about the pivot point, remembering that positive is anticlockwise.
Select Yes, No, Less than, Equal to, or Cannot tell.
If m1 * L2 = m2 * L1, is there a negative torque?
Given particular values of L1, L2, and m1, is it always possible to choose m2 such that the masses have no angularacceleration?
For m1 = m2, does the angularacceleration depend only on L1 / L2 ? (If it depends on the actual values of L1 and L2, put 'no'.)
If m1 = m2, will the masses have an angularacceleration?
Problem Weight is: 1  Tries 0/6  
If L1 = 0.490 m, L2 = 1.18m, m1 = 4.10 kg, and m2 = 3.40 kg, what is the angularacceleration of the beam?
Problem Weight is: 1  Tries 0/6  

Problem 4 
A 1.42 kg particle moves in the xy plane with a velocity of v = (4.26i  3.43j) m/s. Determine the particle's angular momentum when its position vector is r = (1.49i + 2.36j) m. Enter the kcomponent of the angular momentum with correct units.
Problem Weight is: 1  Tries 0/6  

Problem 5 
On a frictionless table, a glob of clay of mass 0.760 kg strikes a bar of mass 0.740 kg perpendicularly at a point 0.290 m from the center of the bar and sticks to it.
a) If the bar is 1.460 m long and the clay is moving at...
...Angular momentum and its properties were devised over time by many of the great minds in physics. Newton and Kepler were probably the two biggest factors in the evolution of angular momentum. Angular momentum is the force which a moving body, following a curved path, has because of its mass and motion. Angular momentum is possessed by rotating objects. Understanding torque is the first step to understandingangular momentum.<br><br>Torque is the angular "version" of force. The units for torque are in Newtonmeters. Torque is observed when a force is exerted on a rigid object pivoted about an axis and. This results in the object rotating around that axis. "The torque ? due to a force F about an origin is an inertial frame defined to be ? ? r x F"1 where r is the vector position of the affected object and F is the force applied to the object.<br><br>To understand angular momentum easier it is wise to compare it to the less complex linear momentum because they are similar in many ways. "Linear momentum is the product of an object's mass and its instantaneous velocity. The angular momentum of a rotating object is given by the product of its angular velocity and its moment of inertia. Just as a moving object's inertial mass is a measure of its resistance to linear...
...m
apart. The maximum tension in the belt is 1855 N. The coefficient of friction is 0.3. The
driver pulley of diameter 120 cm runs at 200 rpm. Calculate:
(i) The power transmitted.
(ii) Torque on each of the two shafts.
4
A steel ball of diameter 150 mm rests centrally over a concrete cube of size 150 mm.
Determine the center of gravity of the system, taking weight of concrete = 25,000 N/m2 and
that of steel 80,000 N/m 2.
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Show that the moment of inertia of a thin circular ring of mass ‘M’ and mean radius ‘R’
with respect to its geometric axis is MR2.
Find the mass moment of inertia of a right circular cone of base radius ‘R’ and mass ‘M’
about the axis of the cone.
A train is uniformly accelerated and passes successive kilometer stones with velocities of
18 Kmph and 36 Kmph respectively. Calculate the velocity when it passes the third
kilometer station. Also find the time taken for each of the two intervals of one kilometer.
A homogeneous sphere of radius of a = 100 mm and weight W = 10 N can rotate freely
about a diameter. If it starts from rest and gains with constant angularacceleration,
angular speed N = 180 rpm, in 12 revolutions, find the action moment.
An automobile moving with a uniform velocity of 40 kmph is...
... It's a hot summer and in the depths of the Toronto Transit Authority's lost and found, 17yearold Duncan is cataloging misplaced belongings. And between Jacob, the cranky old man who runs the place, and the endless dusty boxes overflowing with stuff no one will ever claim, Duncan has just about had enough. Then he finds a little leather book filled with the dark and dirty secrets of a twisted mind, a serial killer stalking his prey in the subway. And Duncan can't stop reading. What would you do with a book like that? How far would you go to catch a madman? This is the teaser to an amazing book I read “Acceleration” By: Graham McNamee.
Duncan the main leading character of the story discovers a journal belonging to what he thinks is a serial killer and he uses his knowledge of profiling as well as the clues from the journal to try to decipher who the serial killer is and who are his intended victims before the serial killer strikes. Duncan is a bad kid that’s been in trouble with the law who has been sent to work at the Toronto Transit Commission's lost and found in order to complete his twomonths of community service. He and his friend Wayne were sentenced to community service after Wayne convinced Duncan to break into a new apartment building to steal an expensive toilet that they could sell to his uncle for some quick cash. The two teens end up getting caught when the toilet falls down the stairs and alerts the cop on duty that night.
At his new job,...
...in Lesson 1 is acceleration. An often confused quantity, acceleration has a meaning much different than the meaning associated with it by sports announcers and other individuals. The definition of acceleration is:
Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.
Sports announcers will occasionally say that a person is accelerating if he/she is moving fast. Yet acceleration has nothing to do with going fast. A person can be moving very fast and still not be accelerating. Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating. The data at the right are representative of a northwardmoving accelerating object. The velocity is changing over the course of time. In fact, the velocity is changing by a constant amount  10 m/s  in each second of time. Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration.
The Meaning of Constant Acceleration
Sometimes an accelerating object will change its velocity by the same amount each second. As mentioned in the previous paragraph, the data table above show an object changing its velocity by 10 m/s in each consecutive second. This is referred to as aconstant...
...Acceleration from Gravity on an Incline
I. Introduction:
Acceleration is the rate of change of the velocity of a moving body. Galileo was the first person to actually experiment and examine the concept of acceleration back in the seventeenth century. Acceleration can be determined by calculating the gravity and an incline. An incline is slope that is deviated between horizontal and vertical positions. Gravity is the natural force of attraction towards the center of the earth. Because of this, we are able to calculate acceleration.
II. Purpose:
The purpose of this experiment was to determine the relationship between the angle of an incline and the acceleration of a cart rolling down a ramp. Once our results were recorded, we were able to examine them to determine if our results were based upon gravity’s natural pull.
III. Procedure/Materials
First, we began by setting up our ramp and cart. We then used a motion detector and repeated our experiment five different times each with a different incline to roll the cart down. We recorded data after each time.
Lab Quest
Track
Dynamics Kit
Ring Stand
Vernier Motion Detector
Meter Stick
Calculator
IV. Data
Height, h (cm)
Length, x (cm)
Sin Ѳ
Acceleration Trial 1
(m/s2)
Acceleration Trial 2
(m/s2)
Acceleration Trial 3
(m/s2)
Average Acceleration
(m/s2)
10...
...exerted upon a 60 kg mass for 3 seconds, how much impulse does the mass experience?
7. An 80kg man and his car are suddenly accelerated from rest to a speed of 5 m/s as a result of a rearend collision. Assuming the time taken to be 0.3s, find:
a) the impulse on the man and
b) the average force exerted on him by the back seat of his car.
8. An airplane propeller is rotating at 1900 rev/min.
a. Compute the propeller's angular velocity in rad/s.
b. How long in seconds does it take for the propeller to turn through 30.0 degrees?
9. A disk with a 1.0m radius reaches a maximum angular speed of 18 rad/s before it stops 30 revolutions after attaining the maximum speed. How long did it take the disk to stop?
10. A net torque of 36 N.m acts on a wheel rotating about a fixed axis for 6 s. During this time the angular speed of the wheel increases from 0 to 12 rad/s. The applied force is then removed, and the wheel comes to rest in 75 s.
a. What is the moment of inertia of the wheel?
b. What is the magnitude of the frictional torque?
c. How many revolutions does the wheel make?
...
...Uniform linear acceleration
Introduction
This topic is about particles which move in a straight line and accelerate uniformly. Problems can vary enormously, so you have to have your wits about you. Problems can be broken down into three main categories:
Constant uniform acceleration
Timespeed graphs
Problems involving two particles
Constant uniform acceleration
Remember what the following variables represent: t = the time ; a = theacceleration ; u = the initial speed ; v = the final speed ; s = the displacement from where the particle started. When the acceleration is negative, it is sometimes called a deceleration or retardation. For example, an acceleration of –3 ms2 is the same as a deceleration (or retardation) of 3 ms2.
• To answer this question, you will need to use the four key formulae intelligently.
They are:
• It is important to know the second of these equations off by heart; the others appear on Page 40 of The Mathematical Tables. Secondly, you may be asked to derive either of the last two equations from the first two. Practise this.
• These four formulae will be useful elsewhere (for example when doing Questions 3 and 4 on projectiles and connected particles).
Timespeed graphs
Remember that the above formulae may be used only while the acceleration is uniform. If a particle speeds up,...
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