Angular motion. Show your work and explain your reasoning. A circular saw 22.0 c
ID: 1418174 • Letter: A
Question
Angular motion. Show your work and explain your reasoning. A circular saw 22.0 cm in diameter starts from rest. In 3.10 s, it acceleration with constant angular acceleration to an angular velocity of +7000 rev/min. Find the angular acceleration as the up in rad/s^2. Through how many radians has it turned during this timespan? The website for one manufacture lists "maximum RPM" for saw. What is the linear speed of a tooth at the edge of a saw blade of diameter 40.0 cm operating at its maximum RPM of 4000? Express your answer in m/s. (Understanding this answer should help you to understand why larger diameter saw blades have lower maximum RPM .) Four flat objects (circular ring, circular disk, square disk, and square ring) have the same mass M and the same outer dimension (circular objects have diameters of 2R and squares have sides of 2R). The small circle at the center of each figure represents the axis of rotation for these objects. This axis of rotation passes through the center of mass and is perpendicular to the plane of the objects. Rank, from greatest to least, the moments of of the objects. Greatest 1___2___3___4___Least OR, The moments of inertia of all objects will be the same. OR, We cannot determine the ranking for moments of inertia of the objects.Explanation / Answer
Q2. Given:
radius of saw blade = r= 22/2=11cm=0.11 m
initial angular velocity = wi = 0 ( as it starts from rest)
final angular velocity = wf= 7000 rev/min= 116.66 rev/s= 732.9 rad/s
time taken = t = 3.1 s
a. angular acceleration = (wf-wi)/t= (732.9-0)/3.1= 236.42 rad/s^2
b. angle covered in radian = 1/2 x angular acceleration x time^2
= 1/2 x 236.42 x 3.1^2 = 1136 radian
c. angular velocity = w= 4000 rpm= 66.66 rps= 418.8 radian /s
linear velocity = v = r x w = 418.8 x 0.2 = 83.76 m/s (0.2m= radius)
d. Moment of Inertia
A.For circular ring = M R^2
B. For circular disc = 0.5 x M R^2
C. For square plane = M (2R)^2/6= 0.66 MR^2
D. for square loop = 4 x M (2R)^2/3 = 5.33 MR^2
From greatest to least
1. D 2. A 3. C 4. B