A wheel of radius 1.5 m rotates at a uniform speed. If a point on the rim of the wheel has a central acceleration of 1.5 m/s ^2. what is the point's tangential speed?
To find the tangential speed of a point on the rim of a rotating wheel, we need to make use of the relationship between tangential speed, radius, and angular speed.
The central acceleration is given by the formula:
a = r * ω^2
Where:
a = central acceleration
r = radius of the wheel
ω = angular speed
In this case, the radius of the wheel is given as 1.5 m, and the central acceleration is given as 1.5 m/s^2.
Now, we can rearrange the formula to solve for ω (angular speed):
ω = √(a / r)
Let's substitute the given values:
ω = √(1.5 m/s^2 / 1.5 m)
ω = √(1 s^(-2))
ω = 1 s^(-1)
The angular speed of the wheel is 1 radian per second.
Now, we can calculate the tangential speed using the formula:
v = r * ω
Plugging in the given radius:
v = 1.5 m * 1 s^(-1)
v = 1.5 m/s
Therefore, the point on the rim of the wheel has a tangential speed of 1.5 m/s.