Uniform Circular Motion

To find the total angle through which the wheel has turned, we use the equation for angular motion: Where: - is the initial angular velocity (0 rad/s, since the wheel starts from rest), - is the final angular velocity (10 rad/s), - is the time (5 seconds). Substituting the values: Thus, the total angle turned is 25 radians.

Forces on the bob:

• The tension force acts towards the center of the circle.
• The gravitational force acts vertically downward.

Since the bob is moving with constant speed, the bob is in equilibrium, and the net force acting on it must be zero. Now, we consider the forces in both directions:

For the vertical direction:

For the horizontal direction:

From the vertical direction equation:

Substitute this value of into the horizontal direction equation:

Simplifying:

Given values:

• Speed
• Radius
• Gravitational acceleration

Substitute these values into the equation:

Now, to find the angle , we take the inverse tangent (arctan) of both sides:

Therefore, the angle made by the wire with the vertical is: radians (option D).

Given:

A particle is in uniform circular motion, completing one full revolution.

Step 1: Understanding Key Concepts

• Displacement: The shortest distance between the initial and final positions. Since the particle returns to the same point, displacement is zero.
• Average Speed: Defined as total distance traveled divided by time. The total distance in one revolution is the circumference, which is not zero.
• Average Velocity: Defined as total displacement divided by time. Since displacement is zero, average velocity is also zero.
• Average Acceleration: Uniform circular motion has a centripetal acceleration, but over one complete revolution, the average acceleration vector sums to zero.

Step 2: Identifying the Incorrect Statement

The incorrect statement is:

"Average speed of the particle is zero." (since speed is always positive in motion).

Answer: The correct option is B.