An automobile wheel with a 9.00-cm radius and the radius to the rim is 7cm, as shown below, rotates at 2.50 rad/s. How fast does a point 6.50 cm from the center travel?
1 cm/s
The wheel and rim radius do not matter, and are just there to confuse you. Multiply 6.50 cm/s by the angular velocity, 2.50 rad/s.
The answer will be in cm/s.
To find the speed of a point 6.50 cm from the center, we can use the equation:
v = ω * r
Where:
v is the linear velocity (speed) of the point
ω is the angular velocity of the wheel
r is the distance from the center to the point
In this case, the angular velocity (ω) is given as 2.50 rad/s, and the distance from the center to the point (r) is 6.50 cm.
Plugging these values into the equation, we get:
v = 2.50 rad/s * 6.50 cm = 16.25 cm/s
Therefore, the speed of the point 6.50 cm from the center is 16.25 cm/s.
To find the speed at which a point 6.50 cm from the center of the wheel travels, we can use the formula for linear velocity:
linear velocity = angular velocity * radius
The angular velocity is given as 2.50 rad/s. However, we need to convert the radius to the rim of the wheel from 7 cm to the radius of the entire wheel, which is 9.00 cm. This is because the speed at which a point on the wheel travels is determined by the radius of the entire wheel.
Now, let's substitute the values into the formula:
linear velocity = 2.50 rad/s * 9.00 cm
Calculating this gives us:
linear velocity = 22.50 cm/s
Therefore, the point 6.50 cm from the center of the wheel travels at a speed of 22.50 cm/s.