Question

at 111111:55\text{ p.m.}55 p.m.55, start text, space, p, point, m, point, end text, thomas ties a weight to the minute hand of a clock. the clockwise torque applied by the weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be modeled by a trigonometric function. the torque peaks 151515 minutes after each whole hour, when the minute hand is pointing directly to the right, at 3\text{ nm}3 nm3, start text, space, n, m, end text (newton metre, the si unit for torque). the minimum torque of -3\text{ nm}−3 nmminus, 3, start text, space, n, m, end text occurs 151515 minutes before each whole hour, when the minute hand is pointing directly to the left. find the formula of the trigonometric function that models the torque \tauτtau applied by the weight ttt minutes after thomas attached the weight. define the function using radians.

Answer 1

The trigonometric function's formula, which simulates the torque (tau) that the weight applied t minutes after Thomas attached it is

$3 Sin (\frac{2\frac{22}{7} }{60} (t-51))$

The angular speed of the minutes hand is

$w = \frac{2 (\frac{22}{7}) }{60}$ rad/min

Following the application of weight, the torque as a function of time t is,

$t= t_{0} sin (w (t-5) min)\\ = (3 Nm) sin ((\frac{2 (\frac{22}{7} }{60} ) rad/min (t-5) min)$

$= (3 Nm) sin ( \frac{2 (\frac{22}{7} }{60} (t-5) rad ) \\= 3 sin (\frac{2 \frac{22}{7} }{60} (t-5)$

What is torque ?

Torque, which is also known as the moment of a force, is the propensity of a force to rotate the body to which it is applied. Force (F) x Distance (r) = Torque is how torque is calculated. The distance (r) between the pivot point and the force's action point. A vector quantity is a torque. As a vector quantity, torque always has a direction that is perpendicular to the plane that contains the vectors of force and displacement.

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