As a bowling ball of radius 14.9 cm rolls down the alley to the right, a frictional force of magnitude 1.43 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 with respect to an axis through the center of the ball, we need to consider the relationship between frictional force and torque.
Torque is defined as the product of a force and the distance from the axis of rotation. In this case, the axis of rotation is through the center of the ball. The frictional torque can be calculated using the following formula:
Torque = force x perpendicular distance from the axis of rotation.
In order to apply this formula, we need to determine the perpendicular distance from the axis of rotation. Since the axis passes through the center of the ball, the perpendicular distance is equal to the radius of the ball.
Given:
Radius of the ball (r) = 14.9 cm = 0.149 m
Frictional force (F) = 1.43 N
Therefore, the frictional torque can be calculated as follows:
Torque = Force x Perpendicular distance from the axis of rotation
= F x r
Substituting the given values:
Torque = 1.43 N x 0.149 m
Now, we can calculate the frictional torque by multiplying the force and the perpendicular distance:
Torque ≈ 0.213 Nm
Therefore, the frictional torque with respect to an axis through the center of the ball is approximately 0.213 Nm.