A stone whirled at the end of a rope 30cm long, makes 10cm complete revolutions in 2seconds.Find A. The anngular velocity in radians per second B. Linear speed
an extra "cm" in there? ... or something strange ...
To find the angular velocity in radians per second and the linear speed, we can use the following equations:
Angular velocity (ω) = θ / t,
Linear speed (v) = ω * r.
Given:
Length of the rope (r) = 30 cm,
Number of complete revolutions (θ) = 10 cm,
Time taken (t) = 2 seconds.
A. Calculate the angular velocity (ω):
First, convert the length of the rope and the number of complete revolutions to meters:
Length of the rope (r) = 30 cm = 0.3 m,
Number of complete revolutions (θ) = 10 cm = 0.1 m.
Now, substitute the values into the formula for angular velocity:
Angular velocity (ω) = θ / t = 0.1 m / 2 sec = 0.05 radians per second (since 1 revolution = 2π radians).
Therefore, the angular velocity of the stone is 0.05 radians per second.
B. Calculate the linear speed (v):
Substitute the values of angular velocity (ω) and the length of the rope (r) into the formula for linear speed:
Linear speed (v) = ω * r = 0.05 radians per second * 0.3 m = 0.015 m/s.
Therefore, the linear speed of the stone is 0.015 m/s.
A. 10rev/2s * 6.28rad/rev = 31.4 rad/s.
B. Circumference = 2pi*r = 6.28 * 30cm = 188.4 cm.
Speed = 188.4cm/rev * 10rev/2s = 942cm/s = 9.42 m/s.