The minute hand of a large clock is 0.50 m long.
(A) Calculate its linear speed at its tip in meters per second. (0.000873 m/s)
(B) Calculate the centripetal acceleration of the tip of the hand. (1.52 x 10-6 m/s2)
(a)The angular velocity of the minute hand: w = D@/Dt = 2p/(3600 sec) = 2p/3600 = 0.001745rad/s
therefore,linear speed=wr=0.001745*0.5=0.0087rad/sec
(b)centripetal acceleration=v^2/r
=[(0.001745*0.5)^2]/0.5
=0.001745*0.001745*0.5
=0.0...3045*0.5
=given answers(1.52x10^-6)
it makes one trip around(2PI radians) per hour, or 3600 seconds
a. w=2PI/3600
speed=wr=2PI*.5/3600
g. a=w^2*r
To calculate the linear speed of the minute hand at its tip, you need to know the angular speed and the distance from the center of rotation to the tip of the hand. In this case, you are given the length of the minute hand, which is the radius of the circular path it moves along.
(A) To calculate the linear speed, use the formula:
Linear Speed = Radius x Angular Speed
The angular speed represents the rate at which the minute hand rotates, measured in radians per second. Since the minute hand completes one full rotation every 60 minutes (or 360 degrees), the angular speed can be calculated as follows:
Angular Speed = (2π radians) / (60 minutes) = π/30 radians per minute
To convert the angular speed to radians per second, divide by 60:
Angular Speed = (π/30 radians per minute) / 60 = π/180 radians per second
Now, substitute the given radius and angular speed into the formula:
Linear Speed = (0.50 m) x (π/180 radians per second)
Linear Speed ≈ 0.02758 m/s
Therefore, the linear speed of the minute hand at its tip is approximately 0.02758 m/s.
(B) To calculate the centripetal acceleration of the tip of the hand, use the formula:
Centripetal Acceleration = (Linear Speed)^2 / Radius
Substitute the given linear speed and radius into the formula:
Centripetal Acceleration = (0.02758 m/s)^2 / 0.50 m
Centripetal Acceleration ≈ 0.001202 m^2/s^2
Therefore, the centripetal acceleration of the tip of the hand is approximately 0.001202 m^2/s^2, or 1.52 x 10^-6 m/s^2.