The sweeping second hand on your wall clock is 24cm long.
a)What is the rotational speed of the second hand?
b)Find the translational speed of the tip of the second hand.
c)Find the rotational acceleration of the second hand.
a) w= (2pi rad)/60 sec = .105rad/s
b) v= wr = .105*24 = 2.52cm/s
c) a= 0
a) w= (2pi rad)/60 sec = .105rad/s
b) v= wr = .105*24 = 2.52cm/s
c) a= 0 rad/s^2
To answer these questions, we will need to use some formulas from rotational motion:
a) The rotational speed of an object is given by the formula:
Rotational speed = 2*pi*r / time
where r is the radius (length of the second hand) and time is the time it takes for one complete revolution. In this case, the time for one complete revolution is 60 seconds, since it takes a minute for the second hand to complete a full revolution.
Substituting the values, we have:
Rotational speed = 2*pi*(24 cm) / (60 s) = 2*3.14*(24 cm) / (60 s) ≈ 7.85 cm/s
So, the rotational speed of the second hand is approximately 7.85 cm/s.
b) The translational speed of the tip of the second hand can be found using the formula:
Translational speed = Rotational speed * radius
Substituting the values, we have:
Translational speed = 7.85 cm/s * 24 cm ≈ 188.4 cm/s
So, the translational speed of the tip of the second hand is approximately 188.4 cm/s.
c) The rotational acceleration of the second hand can be found using the formula:
Rotational acceleration = (final rotational speed - initial rotational speed) / time
Since the initial rotational speed is 0 (since the second hand starts from rest), the formula simplifies to:
Rotational acceleration = final rotational speed / time
Substituting the values, we have:
Rotational acceleration = 7.85 cm/s / 60 s = 0.13 cm/s^2
So, the rotational acceleration of the second hand is approximately 0.13 cm/s^2.
To find the answers to these questions, we need to understand a few concepts related to rotational motion and circular motion.
a) Rotational speed (also known as angular speed) is the angle covered per unit time. It is typically measured in radians per second (rad/s). To find the rotational speed of the second hand, we need to know the time it takes to complete one revolution.
b) Translational speed is the linear speed of an object in circular motion. It is the distance traveled per unit time. To find the translational speed of the tip of the second hand, we need to know the radius or length of the second hand.
c) Rotational acceleration is the rate at which an object's rotational speed changes over time. It is typically measured in radians per second squared (rad/s^2). To find the rotational acceleration of the second hand, we need to know how long it takes for the second hand to reach its maximum speed.
Now, let's apply these concepts to answer the given questions:
a) To find the rotational speed, we need to know the time it takes for the second hand to complete one revolution. Let's assume it takes T seconds for the second hand to complete one revolution. The rotational speed (ω) is given by the formula:
ω = 2π/T
where ω is the angular speed in rad/s, and T is the time in seconds.
b) To find the translational speed, we need to know the length of the second hand. Provided that the sweeping second hand on your wall clock is 24 cm long, and assuming it moves in a circular path, we can consider the length of the second hand as the radius (r) of a circle. The translational speed (v) is given by the formula:
v = rω
where v is the translational speed in cm/s, r is the radius in cm, and ω is the angular speed in rad/s.
c) To find the rotational acceleration, we need to know how long it takes for the second hand to reach its maximum speed. Unfortunately, that information is not provided in the question, so we cannot determine the rotational acceleration without further data.
Note: In order to accurately answer these questions, we need to know the time it takes for the second hand to complete one revolution and/or the time it takes for it to reach its maximum speed.