PS 11 GeneralPhysics I for the Life Sciences. Rotational Motion Dr. Benjamin chan Associate Professor Physics Department february 2014. Questions and Problems for Contemplation. Chapter 8 Questions: 1, 4, 8, 10, 15, 18, 22, 24
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Dr. Benjamin chan
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You can reduce an object to a point and describe its translational motion by considering the motion of this point (called its center of mass)
Consider masses m1, m2, m3, … with coordinates (x1, y1), (x2, y2), (x3, y3), …
xcm = (172 cm)(0.149) = 25.6 cm
ycm = (172 cm)(0.23) = 39.6 cm
Center of mass of swimmer in flight follows projectile motion (parabolic) trajectory
Center of mass of wrench follows constant velocity trajectory
Determine the change in the moment of inertia of a particle as the radius of its orbit doubles
It increases by
MgH = ½ (Mv2 + Iw2)
MgH = ½ Mv2+ ½(2/5)MR2(v/R)2
(1/2 + 1/5) v2 = gH
v = [(10/7)gH]1/2
½ Mv2 = MgH
v = (2gH)1/2
P = W/Dt
P = tDq/Dt = tw
1. A 4 kg mass sits at the origin, and a 10 kg mass sits at x = + 21 m. Where is the center of mass on the x-axis?
(a) + 7 m (b) + 10.5 m (c) + 14 m (d) + 15 m
2. An object moving in a circular path experiences
(a) free fall.
(b) constant acceleration.
(c) linear acceleration.
(d) centripetal acceleration.
3. A boy and a girl are riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular velocity?
a) The boy
b) The girl
c) Both have the same non-zero angular velocity.
d) Both have zero angular velocity.
4. A wheel starts at rest, and has an angular acceleration of 4 rad/s2. Through what angle does it turn in 3 s?
a) 36 rad b) 18 rad c) 12 rad d) 9 rad
5. A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer rim move in 2 s?
a) 314 cm b) 4084 cm c) 8995.5 cm d) 17990.8 cm
6. What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter 70 cm when the bike is moving 8 m/s?
a) 91 m/s2 b) 183 m/s2 c) 206 m/s2 d) 266 m/s2
7. A bicycle is moving 4 m/s. What is the angular speed of a wheel if its radius is 30 cm?
a) 0.36 rad/s b) 1.2 rad/s c) 4.8 rad/s d) 13.3 rad/s
8. An ice skater is in a spin with his arms outstretched. If he pulls in his arms, what happens to his kinetic energy?
a) It increases. b) It decreases.
c) It remains constant but non-zero. d) It remains zero.
9. What is the quantity used to measure an object's resistance to changes in rotation?
a) mass b) moment of inertia
c) linear momentum d) angular momentum
10. A wheel of moment of inertia of 5.00 kg-m2 starts from rest and accelerates under a constant torque of 3.00 N-m for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?
a) 57.6 J b) 64.0 J c) 78.8 J d) 122 J