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.)
7.
s = rθ
r = s/θ = 2.63/1.05 = 2.5 in
10.
a.v. = 2πrad/5sec = 1.26 rad/sec
l.v. = 2π*8in/5sec = 10.05in/sec
13.
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
To solve these problems, you'll need to use some mathematical formulas and concepts related to angles, arc length, and circular motion.
7. To find the radius of the clock, we can use the formula for arc length:
Arc Length = Radius x Angle
Given that the angle is 1.05 radians and the arc length is 2.63 inches, we can rearrange the formula to solve for the radius:
Radius = Arc Length / Angle
Simply divide 2.63 inches by 1.05 radians to find the radius of the clock.
10. To find the angular velocity of the pulley in radians/sec, we can use the formula:
Angular Velocity = 2π x Number of Revolutions / Time
Given that the pulley rotates three times every five seconds, we can substitute these values into the formula to find the angular velocity.
To find the linear velocity, we can use the formula:
Linear Velocity = Radius x Angular Velocity
Since we know the radius is 8 inches and we just calculated the angular velocity, we can multiply these values to find the linear velocity. Additionally, to convert the linear velocity to ft/hr, you will need to apply conversion factors to convert inches to feet and seconds to hours.
13. To find the angular velocity of the Earth in radians/sec, we can use the formula:
Angular Velocity = Linear Velocity / Radius
Given that the Earth travels at 29.79 km/sec and the radius of the orbit is 1.496x10^8 km, we can substitute these values into the formula to find the angular velocity. However, before calculating, you'll need to convert the given values to the same units (e.g., both in kilometers or both in meters) for consistency. Also, note that you need to round to three significant digits.