The minute hand of a wall clock measures 18 cm from its tip to the axis about wh

Question

The minute hand of a wall clock measures 18 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the (a) magnitude and (b) angle from a quarter after the hour to half past, the (c) magnitude and (d) angle for the next half hour, and the (e) magnitude and (f) angle for the hour after that? Give all angles as positive values measured counterclockwise from the +x direction (to the right, or 3 o'clock). (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units

Explanation / Answer

Given

the length of the radius of the minute hand in the wall clock is r = 0.18 m

we know that the minute hand can cover 2pi radians in one trip and the maximum displacemern is 2pi*r

a.b)

angle from the quarter after the hour to half past is

from say 3 to 6, it covers 1/4th of the trip that is

angle is 2pi/4 = pi/2 rad

displacement is s = r*theta = 0.18*pi/2 = 0.2827 m

c.d) Next half an hour is

that is from 6 to 12 it can cover half of the round trip that is

angle is 2pi/2 = pi rad

magnitude is s = r*theta = 0.18*pi = 0.5652 m

e.f) hour after that is

comes to the same position so the magnitude of the displacement is zero and

angle it can cover is 2pi rad

because the displacement is the minimum distance between the stating point and ending point , here both are same.

a.b 0.2827 m , pi/2 rad

c.d 0.5652 m , pi rad

e.f 0 m , 2pi rad

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.