A ball with a radius of 1 centimeter starts rolling down a ramp. The acceleration of the ball is 2 m/s^2. What is the angular speed of the ball after 1 second?
After 1 second, the speed of the ball is 2 m/s. Divide that by the radius (0.01 m) for the angular speed, since
w = V/R
To find the angular speed of the ball after 1 second, we first need to determine its linear speed at that time. Linear speed is the speed at which an object moves in a straight line, while angular speed is the rate at which an object rotates.
We can use the formula for linear speed to calculate it. The formula is given by:
v = u + at
Where:
v = Final linear speed
u = Initial linear speed (which is 0 in this case, as the ball starts from rest)
a = Acceleration
t = Time
Given:
u = 0 m/s (initial speed is 0 as the ball starts from rest)
a = 2 m/s^2 (acceleration)
t = 1 second (time)
Let's plug in the values:
v = 0 + (2 m/s^2) * 1 s
v = 0 + (2 m/s^2) * 1 s
v = 2 m/s
Now that we have the linear speed, we can calculate the angular speed using the equation:
ω = v/r
Where:
ω = Angular speed
v = Linear speed
r = Radius
Given:
v = 2 m/s (linear speed)
r = 0.01 m (radius of the ball, converted from 1 cm to 0.01 m)
Let's substitute the values:
ω = (2 m/s) / 0.01 m
ω = 200 s^(-1)
Therefore, the angular speed of the ball after 1 second is 200 s^(-1).