91Ó°ÊÓ

Problem 59

Objects that are at rest relative to the Earth's surface are in circular motion due to Earth's rotation. (a) What is the radial acceleration of an object at the equator? (b) Is the object's apparent weight greater or less than its weight? Explain. (c) By what percentage does the apparent weight differ from the weight at the equator? (d) Is there any place on Earth where a bathroom scale reading is equal to your true weight? Explain.

Problem 60

A person of mass \(M\) stands on a bathroom scale inside a Ferris wheel compartment. The Ferris wheel has radius \(R\) and angular velocity \(\omega\). What is the apparent weight of the person (a) at the top and (b) at the bottom?

Problem 61

A person rides a Ferris wheel that turns with constant angular velocity. Her weight is \(520.0 \mathrm{N}\). At the top of the ride her apparent weight is \(1.5 \mathrm{N}\) different from her true weight. (a) Is her apparent weight at the top \(521.5 \mathrm{N}\) or \(518.5 \mathrm{N} ?\) Why? (b) What is her apparent weight at the bottom of the ride? (c) If the angular speed of the Ferris wheel is \(0.025 \mathrm{rad} / \mathrm{s},\) what is its radius?

Problem 62

Objects that are at rest relative to Earth's surface are in circular motion due to Earth's rotation. What is the radial acceleration of a painting hanging in the Prado Museum in Madrid, Spain, at a latitude of \(40.2^{\circ}\) North? (Note that the object's radial acceleration is not directed toward the center of the Earth.)

Problem 63

A rotating flywheel slows down at a constant rate due to friction in its bearings. After 1 min, its angular velocity has diminished to 0.80 of its initial value \(\alpha\). At the end of the third minute, what is the angular velocity in terms of the initial value?

Problem 64

The Earth rotates on its own axis once per day \((24.0 \mathrm{h})\) What is the tangential speed of the summit of Mt. Kilimanjaro (elevation 5895 m above sea level), which is located approximately on the equator, due to the rotation of the Earth? The equatorial radius of Earth is \(6378 \mathrm{km}\).

Problem 65

A trimmer for cutting weeds and grass near trees and borders has a nylon cord of 0.23 -m length that whirls about an axle at 660 rad/s. What is the linear speed of the tip of the nylon cord?

Problem 66

A high-speed dental drill is rotating at $3.14 \times 10^{4} \mathrm{rad} / \mathrm{s}$ Through how many degrees does the drill rotate in 1.00 s?

Problem 67

A jogger runs counterclockwise around a path of radius \(90.0 \mathrm{m}\) at constant speed. He makes 1.00 revolution in 188.4 s. At \(t=0,\) he is heading due east. (a) What is the jogger's instantaneous velocity at $t=376.8 \mathrm{s} ?\( (b) What is his instantaneous velocity at \)t=94.2 \mathrm{s} ?$

Problem 68

Two gears \(A\) and \(B\) are in contact. The radius of gear \(A\) is twice that of gear \(B\). (a) When \(A\) 's angular velocity is \(6.00 \mathrm{Hz}\) counterclockwise, what is \(B^{\prime}\) s angular velocity? (b) If \(A\) 's radius to the tip of the teeth is \(10.0 \mathrm{cm},\) what is the linear speed of a point on the tip of a gear tooth? What is the linear speed of a point on the tip of \(B\) 's gear tooth?