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Chapter 8: 8-18Q (page 198)

The angular velocity of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Short Answer

Expert verified

The angular speed will decrease, the linear velocity will point to the top of the wheel, and tangential linear acceleration will point eastward.

Step by step solution

01

Understanding the relation between angular speed and angular acceleration

The angular acceleration is expressed as the term that is equivalent to the variation in angular velocity of the wheel in a unit of time. In the SI system, it is represented in terms of radian per second square.

02

Change in angular speed of the wheel

The following is the diagram of the wheel.

The direction of the angular velocity is toward the left, and linear velocity points toward the top of the wheel. The angular acceleration will act in the opposite direction of the angular velocity because of which the wheel will slow down. So, the angular speed decreases, and the direction of the tangential linear acceleration is toward the south.

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Most popular questions from this chapter

A potter is shaping a bowl on a potter's wheel rotating at a constant angular velocity of 1.6 rev/s (Fig. 8鈥�48). The frictional force between her hands and the clay is 1.5 N. (a) How large is her torque on the wheel if the diameter of the bowl is 9.0 cm? (b) How long would it take for the potter's wheel to stop if the only torque acting on it is due to the potter's hands? The moment of inertia of the wheel and the bowl is \(0.11\;{\rm{kg}} \cdot {{\rm{m}}^{\rm{2}}}\).

FIGURE 8-48

Problem 40

On the basis of the law of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate in order to keep the helicopter stable.

A hammer thrower accelerates the hammer\(\left( {{\bf{mass}} = {\bf{7}}{\bf{.30 kg}}} \right)\)from rest within four full turns (revolutions) and releases it at a speed of\({\bf{26}}{\bf{.5 m/s}}\).Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate (a) the angular acceleration, (b) the (linear) tangential acceleration, (c) the centripetal acceleration just before release, (d) the net force being exerted on the hammer by the athlete just before release, and (e) the angle of this force with respect to the radius of the circular motion. Ignore gravity.

This book has three symmetry axes through its center, all mutually perpendicular. The book鈥檚 moment of inertia would be smallest about which of the three? Explain.

Most of our Solar System鈥檚 mass is contained in the Sun, and the planets possess almost all of the Solar System鈥檚 angular momentum. This observation plays a key role in theories attempting to explain the formation of our Solar System. Estimate the fraction of the Solar System鈥檚 total angular momentum that is possessed by planets using a simplified model which includes only the large outer planets with the most angular momentum. The central Sun (mass\(1.99 \times {10^{30}}\;{\rm{kg}}\), radius\(6.96 \times {10^8}\;{\rm{m}}\)) spins about its axis once every 25 days and the planets Jupiter, Saturn, Uranus, and Neptune move in nearly circular orbits around the Sun with orbital data given in the Table below. Ignore each planet鈥檚 spin about its own axis.

Planet

Mean Distance from Sun\(\left( { \times {{10}^6}\;{\rm{km}}} \right)\)

Orbital Period

(Earth Years)

Mass

\(\left( { \times {{10}^{25}}\;{\rm{kg}}} \right)\)

Jupiter

778

11.9

190

Saturn

1427

29.5

56.8

Uranus

2870

84.0

8.68

Neptune

4500

165

10.2
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