4. A wheel, with radius R= 0.5 m, initially has an angular velocity of 2.5 rev/s, and is slowing down at a rate of 2 rad/s. By the time it stops spinning about its center, what distance will a point on the outer rim have traveled? %3D A) 12 m B) 18 m C) 24 m D) 31 m E) 47 m

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom
Section: Chapter Questions
Problem 31P
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4 only easy way to explain step by step and must use provided formula please
The exam is closed book and closed notes.
v?
Circular motion: ac =
W
Pavr = -
At
= ma;
Weight: Fg = mg,;
g= 9.8 m/s²;
Kinetic energy: K =
m v²;
Potential energy: Ug = mgy
E = Er
E = U+K
v2
= m°r;
Rotational motion:
1 rev = 2n rad;
V = or;
a = ar;
a, =
O = 0o + at:
0 = 0o t+
20a = @? - 0o?
K=
T=rx F;
T=rFsin%;
Στ-Ια;
Ipoint mass = mr?
Idisk =
1
mR²
Ig
2
1
2
+Rin
out
1
Ihoop = mR?
12 ml
mL?
Irodlent) = mL
Irod(center) =
Ipall =
mR?
Ishell = -mR
n3D
dW
P =
dt
W
Pavr=
At
I= Icom + MD²
work: W =T0;
K=-
2
W =
Rolling:
Vcom = Ro
K =
m Veom
2
T= f,R
Fmax = HFn
Incline: F=mgsin0 F mgcos0
Angular momentum:
Lpoint mass = m rxv
L= mrvsin 0;
L=m (r.vy - r,Vz)k
L= Io
m,x1 +m,x2
X com =
m1 +m2
LI = Lr
I 01 =I 202
miy1 +m2y 2
Y com =
m1 +m2
4. A wheel, with radius R= 0.5 m, initially has an angular velocity of 2.5 rev/s, and is slowing down at a rate of 2 rad/s?.
By the time it stops spinning about its center, what distance will a point on the outer rim have traveled?
A) 12 m
B) 18 m
C) 24 m
D) 31 m
E) 47 m
Transcribed Image Text:The exam is closed book and closed notes. v? Circular motion: ac = W Pavr = - At = ma; Weight: Fg = mg,; g= 9.8 m/s²; Kinetic energy: K = m v²; Potential energy: Ug = mgy E = Er E = U+K v2 = m°r; Rotational motion: 1 rev = 2n rad; V = or; a = ar; a, = O = 0o + at: 0 = 0o t+ 20a = @? - 0o? K= T=rx F; T=rFsin%; Στ-Ια; Ipoint mass = mr? Idisk = 1 mR² Ig 2 1 2 +Rin out 1 Ihoop = mR? 12 ml mL? Irodlent) = mL Irod(center) = Ipall = mR? Ishell = -mR n3D dW P = dt W Pavr= At I= Icom + MD² work: W =T0; K=- 2 W = Rolling: Vcom = Ro K = m Veom 2 T= f,R Fmax = HFn Incline: F=mgsin0 F mgcos0 Angular momentum: Lpoint mass = m rxv L= mrvsin 0; L=m (r.vy - r,Vz)k L= Io m,x1 +m,x2 X com = m1 +m2 LI = Lr I 01 =I 202 miy1 +m2y 2 Y com = m1 +m2 4. A wheel, with radius R= 0.5 m, initially has an angular velocity of 2.5 rev/s, and is slowing down at a rate of 2 rad/s?. By the time it stops spinning about its center, what distance will a point on the outer rim have traveled? A) 12 m B) 18 m C) 24 m D) 31 m E) 47 m
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