A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (Fig. P7.8). A drop that breaks loose from the tire on one turn rises vertically 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The radius of the wheel is 0.381 m. (a) Why does the first drop rise higher than the second drop? (b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel’s angular acceleration (assuming it to be constant). Figure P7.8 Problems 8 and 69.
A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (Fig. P7.8). A drop that breaks loose from the tire on one turn rises vertically 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The radius of the wheel is 0.381 m. (a) Why does the first drop rise higher than the second drop? (b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel’s angular acceleration (assuming it to be constant). Figure P7.8 Problems 8 and 69.
Solution Summary: The author explains that the first drop rises higher than the second drop as the tangential velocity of the tire decreases in each subsequent turn.
A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (Fig. P7.8). A drop that breaks loose from the tire on one turn rises vertically 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The radius of the wheel is 0.381 m. (a) Why does the first drop rise higher than the second drop? (b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel’s angular acceleration (assuming it to be constant).
Figure P7.8
Problems 8 and 69.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A pendulum has a 0.4-m-long cord and is given a tangential velocity of 0.2 m/s toward the
vertical from a position 0 = 0.3 rad.
Part A
Determine the equation which describes the angular motion.
Express your answer in terms of the variable t. Express coefficients in radians to three significant figures.
ΜΕ ΑΣΦ
vec
(t)=0.3 cos (4.95t) + 0.101 sin (4.95t)
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Part A
■Review
The uniform 150-lb stone (rectangular block) is being turned over on its side by pulling the
vertical cable slowly upward until the stone begins to tip.
(Figure 1)
If it then falls freely (T = 0) from an essentially balanced at-rest position, determine the speed at which the corner A strikes the pad at B. The stone does not slip at its corner C as it falls. Suppose that height of the stone is
L = 1.2 ft.
Express your answer to three significant figures and include the appropriate units.
?
ft
VA 10.76
S
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Consider the circuit shown in the figure. The battery has emf ε = 69 volts and negligible internal resistance. The inductance is L = 0.4 H and the resistances are R 1 = 12 Ω and R 2 = 9.0 Ω. Initially the switch S is open and no currents flow. Then the switch is closed. After leaving the switch closed for a very long time, it is opened again. Just after it is opened, what is the current in R 1?
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