As a bowling ball of radius 15.9 cm rolls down the alley to the right, a frictional force of magnitude 1.46 N, directed to the left, acts on it. Find the frictional torque with respect to an axis through the center of the ball.
To find the frictional torque acting on the bowling ball, we need to use the formula:
Torque = Force × Radius × sin(θ)
First, let's determine the force acting on the ball. In this case, the frictional force is given as 1.46 N, and it is directed to the left.
Next, we need to calculate the radius of the ball. The radius is given as 15.9 cm, but it is better to convert it to meters. There are 100 cm in 1 meter, so the radius is 0.159 m.
Finally, we need to determine the angle θ between the force vector and the radius vector. In this case, the force is acting to the left, while the radius vector points from the center of the ball to its surface, which means the angle is 180 degrees or π radians.
Now let's apply the values into the formula:
Torque = 1.46 N × 0.159 m × sin(π)
Simplifying the equation:
Torque = 1.46 N × 0.159 m × 0
Since sin(π) is equal to 0, the frictional torque in this case is 0 Nm.
Therefore, the frictional torque acting on the ball, with respect to an axis through the center of the ball, is 0 Nm.