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How do i do them? :l

7. At 2:00 P.M., the angle between the hour and minute hands on a clock is 60° (approximately 1.05 radians). The arc length formed by the two hands is 2.63
inches. What is the radius of the clock in inches? (Round to the nearest tenth.)

10. A pulley with a radius of 8 inches rotates three times every five seconds. Find the angular velocity of the pulley in radians/sec (round to the nearest hundredth). Find the linear velocity to the nearst ft/hr.

13. The Earth travels in a circular orbit around the Sun at 29.79 km/sec. If the radius of the orbit is 1.496x10^8km, what is the angular velocity in radians/sec? (Round to three significant digits.)

  • trigonometry -

    s = rθ
    r = s/θ = 2.63/1.05 = 2.5 in

    a.v. = 2πrad/5sec = 1.26 rad/sec
    l.v. = 2π*8in/5sec = 10.05in/sec

    29.29km/sec / (2π*1.496*10^8 km/rev) * 2πrad/rev = 1.958*10^-7 rad/sec

    check: that is about 371 days/rev. Not too close, but reasonable

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