Question

Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed ω. Complete parts (a) through (c). r=6cm, omega = π /6 radian per sec, t=5 sec (a) What is the angle generated by P in time t? θ =□ radian (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) (b) What is the distance traveled by P along the circle in time t? s=□ cm (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) (c) What is the linear speed of P? v=□ cm per sec (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)

Answer 1

To calculate circular motion parameters for point P, the angle θ is (π/6)*5 radians, the distance traveled s is 5π cm, and the linear speed v is π cm per second.

Step-by-step explanation:

To answer the student's question about circular motion and angular speed:

1. The angle generated by point P in time t can be calculated using the formula θ = ωt. Given the angular speed ω = π/6 radian per second and time t = 5 seconds, the angle θ is (π/6) * 5 radians.
2. The distance traveled by point P along the circle in time t, denoted as s, is the product of the radius r and the angle θ. Since r = 6 cm, s = rθ.
3. The linear speed of point P, denoted by v, is the product of the radius r and the angular speed ω. Hence, v = rω.

SUMUP all the final answers:

• θ = (5π) / 6 radians
• s = (6)(5π) / 6 cm = 5π cm
• v = (6)(π/6) cm/sec = π cm/sec